Journal articles: 'Group Klein'

1

Torriani, Hugo H. "Profinite completions of the fundamental group of the Klein bottle." Czechoslovak Mathematical Journal 35, no. 4 (1985): 511–14. http://dx.doi.org/10.21136/cmj.1985.102044.

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KOHLS, MARTIN, and MÜFİT SEZER. "SEPARATING INVARIANTS FOR THE KLEIN FOUR GROUP AND CYCLIC GROUPS." International Journal of Mathematics 24, no. 06 (June 2013): 1350046. http://dx.doi.org/10.1142/s0129167x13500468.

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We consider indecomposable representations of the Klein four group over a field of characteristic 2 and of a cyclic group of order pm with p, m coprime over a field of characteristic p. For each representation, we explicitly describe a separating set in the corresponding ring of invariants. Our construction is recursive and the separating sets we obtain consist of almost entirely orbit sums and products.

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3

Kobayashi, Masaki. "Hopfield neural networks using Klein four-group." Neurocomputing 387 (April 2020): 123–28. http://dx.doi.org/10.1016/j.neucom.2019.12.127.

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4

Balodi, Mamta, Hua-Lin Huang, and Shiv Datt Kumar. "Finite Majid Algebras Over the Klein Group." Communications in Algebra 42, no. 11 (May 23, 2014): 4962–83. http://dx.doi.org/10.1080/00927872.2013.828739.

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5

AHMADINEZHAD, HAMID. "ON CONJUGACY CLASSES OF THE KLEIN SIMPLE GROUP IN CREMONA GROUP." Glasgow Mathematical Journal 59, no. 2 (June 10, 2016): 395–400. http://dx.doi.org/10.1017/s0017089516000239.

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AbstractWe consider countably many three-dimensional PSL2($\mathbb{F}$7)-del Pezzo surface fibrations over ℙ1. Conjecturally, they are all irrational except two families, one of which is the product of a del Pezzo surface with ℙ1. We show that the other model is PSL2($\mathbb{F}$7)-equivariantly birational to ℙ2×ℙ1. Based on a result of Prokhorov, we show that they are non-conjugate as subgroups of the Cremona group Cr3(ℂ).

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6

Goodman, Jim. "The Klein-Gordon Equation." JOURNAL OF ADVANCES IN PHYSICS 13, no. 2 (March 16, 2017): 4648–50. http://dx.doi.org/10.24297/jap.v13i2.5672.

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Two solutions to the Klein-Gordon equation are found. The existence of a maximum relativistic correction of 2 is thus indicated. The normal relativistic correction is given by the usual solution. A certain Hilbert Space is used to find the solutions using a group theory taught at LSU and the Texas Method of Math also taught at LSU. The usefulness of group theoretical manipulations in Hilbert Space is indicated. A lemma is proved using this group theory that predicts a charge of +/-1 is the only values of charge possible. The usefulness of the second solution to the Klein-Gordon equation of a maximum of 2 for the relativistic correction is basic to the mass predictions in [3]. The fact that the energy reaches mc^2 indicates a dipole spinning at velocity c. The dipole is spinning in a magnetic field created by other particles so it creates charge.

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HIDALGO, RUBEN A., and BERNARD MASKIT. "Fixed points of imaginary reflections on hyperbolic handlebodies." Mathematical Proceedings of the Cambridge Philosophical Society 148, no. 1 (September 28, 2009): 135–58. http://dx.doi.org/10.1017/s0305004109990272.

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AbstractA Klein–Schottky group is an extended Kleinian group, containing no reflections and whose orientation-preserving half is a Schottky group. A dihedral-Klein–Schottky group is an extended Kleinian group generated by two different Klein–Schottky groups, both with the same orientation-preserving half. We provide a structural description of the dihedral-Klein–Schottky groups.Let M be a handlebody of genus g, with a Schottky structure. An imaginary reflection τ of M is an orientation-reversing homeomorphism of M, of order two, whose restriction to its interior is an hyperbolic isometry having at most isolated fixed points. It is known that the number of fixed points of τ is at most g + 1; τ is called a maximal imaginary reflection if it has g + 1 fixed points. As a consequence of the structural description of the dihedral-Klein–Schottky groups, we are able to provide upper bounds for the cardinality of the set of fixed points of two or three different imaginary reflections acting on a handlebody with a Schottky structure. In particular, we show that maximal imaginary reflections are unique.

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8

Saragih, Asido, and Santri Chintia Purba. "Application of Klein-4 Group on Domino Card." International Journal of Applied Sciences and Smart Technologies 02, no. 01 (June 8, 2020): 67–74. http://dx.doi.org/10.24071/ijasst.v2i1.2191.

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9

Lachaud, G. "The Klein Quartic as a Cyclic Group Generator." Moscow Mathematical Journal 5, no. 4 (2005): 857–68. http://dx.doi.org/10.17323/1609-4514-2005-5-4-857-868.

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10

Bujalance, E., A. F. Costa, and J. M. Gamboa. "THE HYPERELLIPTIC MAPPING CLASS GROUP OF KLEIN SURFACES." Proceedings of the Edinburgh Mathematical Society 44, no. 2 (June 2001): 351–63. http://dx.doi.org/10.1017/s0013091599000322.

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AbstractIn this paper we study the algebraic structure of the hyperelliptic mapping class group of Klein surfaces, which is closely related to the mapping class group of punctured discs. This group plays an important role in the study of the moduli space of hyperelliptic real algebraic curves. Our main result provides a presentation by generators and relations for the hyperelliptic mapping class group of surfaces of prescribed topological type.AMS 2000 Mathematics subject classification: Primary 14H10; 20H10; 30F50

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Bujalance, E., J. A. Bujalance, and E. Martínez. "On the automorphism group of hyperelliptic Klein surfaces." Michigan Mathematical Journal 35, no. 3 (1988): 361–68. http://dx.doi.org/10.1307/mmj/1029003817.

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12

Le Roux, Frédéric. "Free planar actions of the Klein bottle group." Geometry & Topology 15, no. 3 (September 5, 2011): 1545–67. http://dx.doi.org/10.2140/gt.2011.15.1545.

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13

Boboc, Crina. "Gradings of Matrix Algebras by the Klein Group." Communications in Algebra 31, no. 5 (January 6, 2003): 2311–26. http://dx.doi.org/10.1081/agb-120018999.

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14

Rudra, P. "Symmetry group of the nonlinear Klein-Gordon equation." Journal of Physics A: Mathematical and General 19, no. 13 (September 11, 1986): 2499–504. http://dx.doi.org/10.1088/0305-4470/19/13/015.

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15

Stevens, Brett. "Recursive construction of maximum number of non-overlapping Klein 4-groups inside an elementary Abelian 2-group." Tamkang Journal of Mathematics 41, no. 4 (November 23, 2010): 349–51. http://dx.doi.org/10.5556/j.tkjm.41.2010.500.

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16

Gordejuela, J. J. Etayo. "On the order of automorphism groups of Klein surfaces." Glasgow Mathematical Journal 26, no. 1 (January 1985): 75–81. http://dx.doi.org/10.1017/s0017089500005796.

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A problem of special interest in the study of automorphism groups of surfaces are the bounds of the orders of the groups as a function of the genus of the surface.May has proved that a Klein surface with boundary of algebraic genus p has at most 12(p–1) automorphisms [9].In this paper we study the highest possible prime order for a group of automorphisms of a Klein surface. This problem was solved for Riemann surfaces by Moore in [10]. We shall use his results for studying the Klein surfaces that are not Riemann surfaces. The more general result that we obtain is the following: if X is a Klein surface of algebraic genus p, and G is a group of automorphisms of X, of prime order n, then n ≤ p + 1.

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17

Singerman, David. "Orientable and non-orientable Klein surfaces with maximal symmetry." Glasgow Mathematical Journal 26, no. 1 (January 1985): 31–34. http://dx.doi.org/10.1017/s0017089500005747.

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Let X be a bordered Klein surface, by which we mean a Klein surface with non-empty boundary. X is characterized topologically by its orientability, the number k of its boundary components and the genus p of the closed surface obtained by filling in all the holes. The algebraic genus g of X is defined by.If g≥2 it is known that if G is a group of automorphisms of X then |G|≤12(g-l) and that the upper bound is attained for infinitely many values of g ([4], [5]). A bordered Klein surface for which this upper bound is attained is said to have maximal symmetry. A group of 12(g-l) automorphisms of a bordered Klein surface of algebraic genus g is called an M*-group and it is known that a finite group G is an M*-group if and only if it is generated by 3 non-trivial elements T1, T2, T3 which obey the relations([4]).

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18

Bujalance, E., A. F. Costa, G. Gromadzki, and D. Singerman. "Automorphism groups of complex doubles of Klein surfaces." Glasgow Mathematical Journal 36, no. 3 (September 1994): 313–30. http://dx.doi.org/10.1017/s0017089500030925.

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In this paper we consider complex doubles of compact Klein surfaces that have large automorphism groups. It is known that a bordered Klein surface of algebraic genus g > 2 has at most 12(g − 1) automorphisms. Surfaces for which this bound is sharp are said to have maximal symmetry. The complex double of such a surface X is a compact Riemann surface X+ of genus g and it is easy to see that if G is the group of automorphisms of X then C2 × G is a group of automorphisms of X+. A natural question is whether X+ can have a group that strictly contains C2 × G. In [8] C. L. May claimed the following interesting result: there is a unique Klein surface X with maximal symmetry for which Aut X+ properly contains C2 × Aut X (where Aut X+ denotes the group of conformal and anticonformal automorphisms of X+).

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19

Kramer, P. "Fricke-Klein geometry for the group Sl(2,C)." Journal of Physics A: Mathematical and General 26, no. 5 (March 7, 1993): L245—L250. http://dx.doi.org/10.1088/0305-4470/26/5/013.

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20

Schain, Joan. "Can Klein and Kohut work together in a group?" Clinical Social Work Journal 13, no. 4 (1985): 293–304. http://dx.doi.org/10.1007/bf00755365.

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21

Hidber, Cristhian E., and Daniel Juan-Pineda. "The algebraic K-theory of the group ring of the Klein bottle group." Topology and its Applications 293 (April 2021): 107562. http://dx.doi.org/10.1016/j.topol.2020.107562.

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22

MAY, COY L. "THE REAL GENUS OF 2-GROUPS." Journal of Algebra and Its Applications 06, no. 01 (February 2007): 103–18. http://dx.doi.org/10.1142/s0219498807002090.

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Let G be a finite group. The real genus ρ(G) is the minimum algebraic genus of any compact bordered Klein surface on which G acts. Here we consider 2-groups acting on bordered Klein surfaces. The main focus is determining the real genus of each of the 51 groups of order 32. We also obtain some general results about the partial presentations that 2-groups acting on bordered surfaces must have. In addition, we obtain genus formulas for some families of 2-groups and show that if G is a 2-group with positive real genus, then ρ(G) ≡ 1 mod 4.

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23

Wallace, D. A. R. "On the automorphism group of the integral group ring of the infinite dihedral group." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 108, no. 1-2 (1988): 1–10. http://dx.doi.org/10.1017/s0308210500026469.

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SynopsisLet ℤ(G) be the integral group ring of the infinite dihedral groupG; the aim is to calculate Autℤ(G), the group of Z-linear automorphisms of ℤ(G). It is shown that Aut ℤ(G), the subgroup of Aut *ℤ(G) consisting of those automorphisms that preserve elementwise the centre of ℤ(G), is a normal subgroup of Aut *ℤ(G) of index 2 and that Aut*ℤ(G) may be embedded monomorphically intoM2(ℤ[t]), the ring of 2 × 2 matrices over a polynomial ring ℤ[t]From this embedding and by the Noether—Skolem Theorem it is shown that Inn (G), the group of inner automorphisms of ℤ(G) induced by the units of ℤ(G), is a normal subgroup of Aut*ℤ(G)/ such that Aut*ℤ(G)/Inn (G) is isomorphic to the Klein four-group.

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24

Torriani, Hugo H. "Faithful integral and modular representations of the Klein bottle group." Colloquium Mathematicum 54, no. 1 (1987): 71–75. http://dx.doi.org/10.4064/cm-54-1-71-75.

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25

Craven, David A., Charles W. Eaton, Radha Kessar, and Markus Linckelmann. "The structure of blocks with a Klein four defect group." Mathematische Zeitschrift 268, no. 1-2 (February 11, 2010): 441–76. http://dx.doi.org/10.1007/s00209-010-0679-4.

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Cheltsov, Ivan, and Constantin Shramov. "Three embeddings of the Klein simple group into the Cremona group of rank three." Transformation Groups 17, no. 2 (April 17, 2012): 303–50. http://dx.doi.org/10.1007/s00031-012-9183-8.

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27

Obukhov, Valeriy V. "Algebra of Symmetry Operators for Klein-Gordon-Fock Equation." Symmetry 13, no. 4 (April 20, 2021): 727. http://dx.doi.org/10.3390/sym13040727.

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All external electromagnetic fields in which the Klein-Gordon-Fock equation admits the first-order symmetry operators are found, provided that in the space-time V4 a group of motion G3 acts simply transitively on a non-null subspace of transitivity V3. It is shown that in the case of a Riemannian space Vn, in which the group Gr acts simply transitively, the algebra of symmetry operators of the n-dimensional Klein-Gordon-Fock equation in an external admissible electromagnetic field coincides with the algebra of operators of the group Gr.

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López-Ruiz, Francisco F., Julio Guerrero, and Victor Aldaya. "Invariant Scalar Product and Associated Structures for Tachyonic Klein–Gordon Equation and Helmholtz Equation." Symmetry 13, no. 7 (July 20, 2021): 1302. http://dx.doi.org/10.3390/sym13071302.

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Although describing very different physical systems, both the Klein–Gordon equation for tachyons (m2<0) and the Helmholtz equation share a remarkable property: a unitary and irreducible representation of the corresponding invariance group on a suitable subspace of solutions is only achieved if a non-local scalar product is defined. Then, a subset of oscillatory solutions of the Helmholtz equation supports a unirrep of the Euclidean group, and a subset of oscillatory solutions of the Klein–Gordon equation with m2<0 supports the scalar tachyonic representation of the Poincaré group. As a consequence, these systems also share similar structures, such as certain singularized solutions and projectors on the representation spaces, but they must be treated carefully in each case. We analyze differences and analogies, compare both equations with the conventional m2>0 Klein–Gordon equation, and provide a unified framework for the scalar products of the three equations.

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TANAKA, IZUMI, and SEIJI NAGAMI. "GAUGE GROUP AND TOPOLOGY CHANGE." International Journal of Geometric Methods in Modern Physics 08, no. 06 (September 2011): 1225–38. http://dx.doi.org/10.1142/s0219887811005622.

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The purpose of this study is to examine the effect of topology change in the initial universe. In this study, the concept of G-cobordism is introduced to argue about the topology change of the manifold on which a transformation group acts. This G-manifold has a fiber bundle structure if the group action is free and is related to the spacetime in Kaluza–Klein theory or Einstein–Yang–Mills system. Our results revealed the fundamental processes of compactification in G-manifolds. In these processes, the initial high symmetry and multidimensional universe changes to present universe by the mechanism which lowers the dimensions and symmetries.

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May, Coy L. "A Family of M*-Groups." Canadian Journal of Mathematics 38, no. 5 (October 1, 1986): 1094–109. http://dx.doi.org/10.4153/cjm-1986-054-8.

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A compact bordered Klein surface of (algebraic) genus g ≦ 2 is said to have maximal symmetry [5] if its automorphism group is of order 12(g – 1), the largest possible. An M*-group acts as the automorphism group of a bordered surface with maximal symmetry. M*-groups were first studied in [6], and additional results about these groups are in [5, 7, 8].Here we construct a new, interesting family of M*-groups. Each group G in the family is an extension of a cyclic group by the automorphism group of a torus T with holes that has maximal symmetry. Furthermore, G acts on a bordered Klein surface X that is a fully wound covering [7] of T, that is, an especially nice covering in which X has the same number of boundary components as T. The construction we use for the new family of M*-groups is a standard one that employs group automorphisms to define extensions of groups.

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31

Dobbs, David E. "On the maximal number of non-overlapping Klein 4-groups inside an elementary abelian 2-group." Tamkang Journal of Mathematics 40, no. 2 (June 30, 2009): 113–16. http://dx.doi.org/10.5556/j.tkjm.40.2009.460.

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Let $G$ be a finite elementary abelian $2$-group of order $2^n$, for some integer $n \geq 2$. Let $b_n$ be the maximal cardinality of a set ${\mathcal S}$ of subgroups of $G$ such that each member of ${\mathcal S}$ is isomorphic to the Klein $4$-group and any two distinct members of ${\mathcal S}$ meet only in $0$. It is proved that $b_{n+2} \geq 4b_n$. Consequently, $b_n \geq 2^{n-2}$ if $n$ is even, while $b_n \geq 2^{n-3}$ if $n$ is odd; these results are best possible since $b_2=1=b_3$.

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32

Matsuura, Atsushi. "The automorphism group of the Klein curve in the mapping class group of genus $3$." Proceedings of the Japan Academy, Series A, Mathematical Sciences 72, no. 7 (1996): 139–40. http://dx.doi.org/10.3792/pjaa.72.139.

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33

PARVATHI, M., and B. SIVAKUMAR. "THE KLEIN-4 DIAGRAM ALGEBRAS." Journal of Algebra and Its Applications 07, no. 02 (April 2008): 231–62. http://dx.doi.org/10.1142/s0219498808002795.

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In this paper we study a new class of diagram algebras, the Klein-4 diagram algebras denoted by Rk(n). These algebras are the centralizer algebras of the group Gn := (ℤ2 × ℤ2)≀Sn acting on V⊗k, where V is the signed permutation module for Gn These algebras have been realized as subalgebras of the extended G-vertex colored partition algebras introduced by Parvathi and Kennedy in [7]. In this paper we give a combinatorial rule for the decomposition of the tensor powers of the signed permutation representation of Gn by explicitly constructing the basis for the irreducible modules. In the process we also give the basis for the irreducible modules appearing in the decomposition of V⊗k in [5]. We then use this rule to describe the Bratteli diagram of Klein-4 diagram algebras.

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Natarajan, Lakshmi Prasad, and B. Sundar Rajan. "Low ML Decoding Complexity STBCs via Codes Over the Klein Group." IEEE Transactions on Information Theory 57, no. 12 (December 2011): 7950–71. http://dx.doi.org/10.1109/tit.2011.2170113.

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35

Sezer, Müfit, and R. James Shank. "Rings of invariants for modular representations of the Klein four group." Transactions of the American Mathematical Society 368, no. 8 (December 3, 2015): 5655–73. http://dx.doi.org/10.1090/tran/6516.

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36

Pforte, Lars, and John Murray. "The indecomposable symplectic and quadratic modules of the Klein-four group." Journal of Algebra 505 (July 2018): 92–124. http://dx.doi.org/10.1016/j.jalgebra.2018.02.032.

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37

Linckelmann, M. "The Source Algebras of Blocks with a Klein Four Defect Group." Journal of Algebra 167, no. 3 (August 1994): 821–54. http://dx.doi.org/10.1006/jabr.1994.1214.

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38

Bujalance, E., J. M. Gamboa, and C. Maclachlan. "Minimum topological genus of compact bordered Klein surfaces admitting a prime-power automorphism." Glasgow Mathematical Journal 37, no. 2 (May 1995): 221–32. http://dx.doi.org/10.1017/s0017089500031128.

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In the nineteenth century, Hurwitz [8] and Wiman [14] obtained bounds for the order of the automorphism group and the order of each automorphism of an orientable and unbordered compact Klein surface (i. e., a compact Riemann surface) of topological genus g s 2. The corresponding results of bordered surfaces are due to May, [11], [12]. These may be considered as particular cases of the general problem of finding the minimum topological genus of a surface for which a given finite group G is a group of automorphisms. This problem was solved for cyclic and abelian G by Harvey [7] and Maclachlan [10], respectively, in the case of Riemann surfaces and by Bujalance [2], Hall [6] and Gromadzki [5] in the case of non-orientable and unbordered Klein surfaces. In dealing with bordered Klein surfaces, the algebraic genus—i. e., the topological genus of the canonical double covering, (see Alling-Greenleaf [1])—was minimized by Bujalance- Etayo-Gamboa-Martens [3] in the case where G is cyclic and by McCullough [13] in the abelian case.

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Muatjetjeja, B. "Group classification and conservation laws of the generalized Klein–Gordon–Fock equation." International Journal of Modern Physics B 30, no. 28n29 (November 10, 2016): 1640023. http://dx.doi.org/10.1142/s0217979216400233.

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In the present paper, we perform Lie and Noether symmetries of the generalized Klein–Gordon–Fock equation. It is shown that the principal Lie algebra, which is one-dimensional, has several possible extensions. It is further shown that several cases arise for which Noether symmetries exist. Exact solutions for some cases are also obtained from the invariant solutions of the investigated equation.

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Nisticò, Giuseppe. "Group Theoretical Derivation of Consistent Free Particle Theories." Foundations of Physics 50, no. 9 (August 14, 2020): 977–1007. http://dx.doi.org/10.1007/s10701-020-00364-2.

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AbstractThe difficulties of relativistic particle theories formulated by means of canonical quantization, such as those of Klein–Gordon and Dirac, ultimately led theoretical physicists to turn to quantum field theory to model elementary particle physics. In order to overcome these difficulties, the theories of the present approach are developed deductively from the physical principles that specify the system, without making use of canonical quantization. For a free particle these starting assumptions are invariance of the theory and covariance of position with respect to Poincaré transformations. In pursuing the approach, the effectiveness of group theoretical methods is exploited. The coherent development of our program has shown that robust classes of representations of the Poincaré group, discarded by the known particle theories, can in fact be taken as bases for perfectly consistent theories. For massive spin zero particles, six inequivalent theories have been determined, two of which do not correspond to any of the current ones; all of these theories overcome the difficulties of Klein–Gordon one. The present lack of the explicit transformation properties of position with respect to boosts prevents the complete determination of non zero spin particle theories. In the past a particular form of these transformation properties was adopted by Jordan and Mukunda. We check its consistency within the present approach and find that for spin $$\frac{1}{2}$$ 1 2 particles there is only one consistent theory, which is unitarily related to Dirac’s; yet, once again, it requires classes of irreducible representations previously discarded.

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LINARES, ROMAN. "BIANCHI IX GROUP-MANIFOLD REDUCTIONS OF GRAVITY." Modern Physics Letters A 20, no. 40 (December 28, 2005): 3115–25. http://dx.doi.org/10.1142/s0217732305018670.

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We exhibit a new way to perform the group-manifold reduction of pure Einstein gravity in the vielbein formulation when the compactification group manifold is S3. The new Bianchi IX group-manifold reduction is obtained by exploiting the two three-dimensional Lie algebras that the S3 group manifold admits. As an application of the new reduction we show that there exists a domain wall solution to the lower-dimensional theory which upon uplifting to the higher-dimension turns out to be the self-dual (in the nonvanishing components of both curvature and spin connection) Kaluza–Klein monopole.

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Gilligan, Bruce. "On closed radical orbits in homogeneous complex manifolds." Bulletin of the Australian Mathematical Society 54, no. 3 (December 1996): 363–68. http://dx.doi.org/10.1017/s0004972700021766.

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Suppose G is a complex Lie group having a finite number of connected components and H is a closed complex subgroup of G with H° solvable. Let RG denote the radical of G. We show the existence of closed complex subgroups I and J of G containing H such that I/H is a connected solvmanifold with I° ⊃ RG, the space G/J has a Klein form SG/A, where A is an algebraic subgroup of the semisimple complex Lie group SG: = G/RG, and, unless I = J, the space J/I has Klein form , where is a Zariski dense discrete subgroup of some connected positive dimensional semisimple complex Lie group Ŝ.

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Bujalance, J. A., and B. Estrada. "q-hyperelliptic compact nonorientable Klein surfaces without boundary." International Journal of Mathematics and Mathematical Sciences 31, no. 4 (2002): 215–27. http://dx.doi.org/10.1155/s0161171202109173.

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LetXbe a nonorientable Klein surface (KS in short), that is a compact nonorientable surface with a dianalytic structure defined on it. A Klein surfaceXis said to beq-hyperellipticif and only if there exists an involutionΦonX(a dianalytic homeomorphism of order two) such that the quotientX/〈Φ〉has algebraic genusq.q-hyperelliptic nonorientable KSs without boundary (nonorientable Riemann surfaces) were characterized by means of non-Euclidean crystallographic groups. In this paper, using that characterization, we determine bounds for the order of the automorphism group of a nonorientableq-hyperelliptic Klein surfaceXsuch thatX/〈Φ〉has no boundary and prove that the bounds are attained. Besides, we obtain the dimension of the Teichmüller space associated to this type of surfaces.

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HANLON, B. E., and G. C. JOSHI. "SPONTANEOUS CP VIOLATION FROM A QUATERNIONIC KALUZA–KLEIN THEORY." International Journal of Modern Physics A 08, no. 19 (July 30, 1993): 3263–83. http://dx.doi.org/10.1142/s0217751x93001314.

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Motivated by the isomorphism between the universal covering group of the six-dimensional Lorentz group and the special linear group over the quaternions, a locally quaternionic covariant theory is postulated to exist in six space–time dimensions. Compactifying onto the space–time M4 ⊗ S2 a complex theory is retrieved on the four-dimensional Minkowski space with the essential quaternionic nature confined to S2. Quaternionic spinors are introduced and a dimensionally reduced theory recovered which exhibits a CP-violating effect via spontaneous symmetry breaking.

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Deraux, Martin. "Non-arithmetic lattices and the Klein quartic." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 754 (September 1, 2019): 253–79. http://dx.doi.org/10.1515/crelle-2017-0005.

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Abstract We give an algebro-geometric construction of some of the non-arithmetic ball quotients constructed by the author, Parker and Paupert. The new construction reveals a relationship between the corresponding orbifold fundamental groups and the automorphism group of the Klein quartic, and also with groups constructed by Barthel–Hirzebruch–Höfer and Couwenberg–Heckman–Looijenga.

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MANTICA, Giorgio. "PLATO, APOLLONIUS, AND KLEIN: Playing with Spheres." International Journal of Modern Physics C 04, no. 02 (April 1993): 345–55. http://dx.doi.org/10.1142/s0129183193000379.

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We show that a large class of circle packings can be generated by combining hyperbolic and spherical (or Euclidean) tessellation groups. We provide the general group-theoretical framework associated to an efficient, geometrically inspired, construction of these packings. We classify the different packings that can be obtained in this way, and we investigate their fractal properties.

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Harlander, Jens, and Andrew Misseldine. "On the $K$-theory and homotopy theory of the Klein bottle group." Homology, Homotopy and Applications 13, no. 2 (2011): 63–72. http://dx.doi.org/10.4310/hha.2011.v13.n2.a5.

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Okada, Takuzo. "Nonrational del Pezzo fibrations admitting an action of the Klein simple group." European Journal of Mathematics 2, no. 1 (October 30, 2015): 319–32. http://dx.doi.org/10.1007/s40879-015-0080-2.

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Som, Abhishek, and Sourin Das. "Enhancement of superluminal weak values under Lorentz boost." Modern Physics Letters A 35, no. 34 (September 16, 2020): 2050279. http://dx.doi.org/10.1142/s021773232050279x.

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The local group velocity defined as the weak value of the velocity operator in (1 + 1)-dimensional Klein-Gordon and Dirac theory is studied. As shown by Berry [J. Phys. A 45, 185308 (2012)], when the pre- and post-selected states for evaluating the weak value are chosen at random from an ensemble of available states, it gives rise to a universal probability distribution for the local group velocity which can have both subluminal and superluminal components. In this work, we explore the possibility of enhancement of the superluminal fraction of this total probability distribution by applying a Lorentz boost and show that it can indeed be enhanced both in the case of Klein–Gordon and Dirac theories.

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Tsok, Samuel. "Application of Group Theory to a Local Game Called “Tsorry Checkerboard” (A Case of Klein Four- Group)." IOSR Journal of Mathematics 7, no. 3 (2013): 04–06. http://dx.doi.org/10.9790/5728-0730406.

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Journal articles on the topic 'Group Klein'

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