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Journal articles on the topic 'Nonabelian class field theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 27 July 2025

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1

Kim, Kwang-Seob, and John C. Miller. "Class numbers of large degree nonabelian number fields." Mathematics of Computation 88, no. 316 (2018): 973–81. http://dx.doi.org/10.1090/mcom/3335.

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2

BIRÓ, T. S. "CONSERVING ALGORITHMS FOR REAL-TIME NONABELIAN LATTICE GAUGE THEORIES." International Journal of Modern Physics C 06, no. 03 (1995): 327–44. http://dx.doi.org/10.1142/s0129183195000241.

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A class of numerical algorithms for solving the classical equations of motion in lattice gauge field theories which exactly fulfill the constraints imposed by the unitarity of the local group elements, by the local color charge conservation (Gauss law) and by the total energy conservation is constructed. The performance of these constrained algorithms is comparatively discussed.

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3

BAGIŃSKI, CZESŁAW, and JÁNOS KURDICS. "ON THE CENTER OF THE MODULAR GROUP ALGEBRA OF A FINITE p-GROUP." Journal of Algebra and Its Applications 13, no. 04 (2014): 1350127. http://dx.doi.org/10.1142/s0219498813501272.

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Let G be a finite nonabelian p-group and F a field of characteristic p and let [Formula: see text] be the subalgebra spanned by class sums [Formula: see text], where C runs over all conjugacy classes of noncentral elements of G. We show that all finite p-groups are subgroups and homomorphic images of p-groups for which [Formula: see text]. We also give the description of abelian-by-cyclic groups for which [Formula: see text] is an algebra with zero multiplication or is nil of index 2.

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4

SBEITY, FARAH, and BOUCHAÏB SODAÏGUI. "CLASSES DE STEINITZ D'EXTENSIONS NON ABÉLIENNES À GROUPE DE GALOIS D'ORDRE 16 OU EXTRASPÉCIAL D'ORDRE 32 ET PROBLÈME DE PLONGEMENT." International Journal of Number Theory 06, no. 08 (2010): 1769–83. http://dx.doi.org/10.1142/s1793042110003794.

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Soient k un corps de nombres et Cl (k) son groupe des classes. Soit Γ un groupe non abélien d'ordre 16, ou un groupe extraspécial d'ordre 32. Soit Rm(k, Γ) le sous-ensemble de Cl (k) formé par les éléments qui sont réalisables par les classes de Steinitz d'extensions galoisiennes de k, modérément ramifiées et dont le groupe de Galois est isomorphe à Γ. Lorsque Γ est le groupe modulaire d'ordre 16, on suppose que k contienne une racine primitive 4ème de l'unité. Dans cet article on montre que Rm(k, Γ) est le groupe Cl (k) tout entier si le nombre des classes de k est impair. On étudie un problè

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5

Bacon, Michael R. "On the non-albelian tensor square of a nilpotent group of class two." Glasgow Mathematical Journal 36, no. 3 (1994): 291–96. http://dx.doi.org/10.1017/s0017089500030883.

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The nonabelian tensor square G⊗G of a group G is generated by the symbols g⊗h, g, h ∈ G, subject to the relations,for all g, g′, h, h′ ∈ G, where The tensor square is a special case of the nonabelian tensor product which has its origins in homotopy theory. It was introduced by R. Brown and J. L. Loday in [4] and [5], extending ideas of Whitehead in [6].

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6

Pirashvili, Mariam. "Second cohomotopy and nonabelian cohomology." Journal of K-theory 13, no. 3 (2014): 397–445. http://dx.doi.org/10.1017/is013012015jkt251.

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AbstractThe main difficulty in the theory of non-abelian cohomology is that for cosimplicial groups only zero-th and first dimensional cohomotopy are known. In this article we introduce a new class of cosimplicial groups, called centralised cosimplicial groups, for which we are able to define a second cohomotopy, with all expected properties. The main examples of such cosimplicial groups come from 2-categories.

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7

Coletti, Erasmo, Ilya Sigalov, and Washington Taylor. "Abelian and nonabelian vector field effective actions from string field theory." Journal of High Energy Physics 2003, no. 09 (2003): 050. http://dx.doi.org/10.1088/1126-6708/2003/09/050.

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8

Qian, Guohua, and Yong Yang. "The largest conjugacy class size and the nilpotent subgroups of finite groups." Journal of Group Theory 22, no. 2 (2019): 267–76. http://dx.doi.org/10.1515/jgth-2018-0040.

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AbstractLetHbe a nilpotent subgroup of a finite nonabelian groupG, let{\pi=\pi(|H|)}and let{{\operatorname{bcl}}(G)}be the largest conjugacy class size of the groupG. In the present paper, we show that{|HO_{\pi}(G)/O_{\pi}(G)|<{\operatorname{bcl}}(G)}.

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9

Bak, Anthony. "Nonabelian K-theory: The nilpotent class of K1 and general stability." K-Theory 4, no. 4 (1991): 363–97. http://dx.doi.org/10.1007/bf00533991.

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10

LÓPEZ PEÑA, J., S. MAJID, and K. RIETSCH. "Lie theory of finite simple groups and the Roth property." Mathematical Proceedings of the Cambridge Philosophical Society 163, no. 2 (2017): 301–40. http://dx.doi.org/10.1017/s030500411600102x.

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AbstractIn noncommutative geometry a ‘Lie algebra’ or bidirectional bicovariant differential calculus on a finite group is provided by a choice of an ad-stable generating subset $\mathcal{C}$ stable under inversion. We study the associated Killing form K. For the universal calculus associated to $\mathcal{C}$ = G \ {e} we show that the magnitude $\mu=\sum_{a,b\in\mathcal{C}}(K^{-1})_{a,b}$ of the Killing form is defined for all finite groups (even when K is not invertible) and that a finite group is Roth, meaning its conjugation representation contains every irreducible, iff μ ≠ 1/(N − 1) wher

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11

Balatsky, Alexander. "Spin Singlet Quantum Hall Effect and Nonabelian Landau-Ginzburg Theory." International Journal of Modern Physics B 06, no. 05n06 (1992): 765–88. http://dx.doi.org/10.1142/s0217979292000463.

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In this paper we present a theory of Singlet Quantum Hall Effect (SQHE). We show that the Halperin-Haldane SQHE wave function can be written in the form of a product of a wave function for charged semions in a magnetic field and a wave function for the Chiral Spin Liquid of neutral spin-½ semions. We introduce field-theoretic model in which the electron operators are factorized in terms of charged spinless semions (holons) and neutral spin-½ semions (spinons). Broken time reversal symmetry and short ranged spin correlations lead to SU(2)k=1 Chern-Simons term in Landau-Ginzburg action for SQHE

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12

Biswas, Indranil, та Olivier Serman. "A Torelli theorem for moduli spaces of principal bundles on curves defined over ℝ". International Journal of Mathematics 28, № 06 (2017): 1750049. http://dx.doi.org/10.1142/s0129167x17500495.

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Let [Formula: see text] be a geometrically irreducible smooth projective curve, of genus at least three, defined over the field of real numbers. Let [Formula: see text] be a connected reductive affine algebraic group, defined over [Formula: see text], such that [Formula: see text] is nonabelian and has one simple factor. We prove that the isomorphism class of the moduli space of principal [Formula: see text]-bundles on [Formula: see text] determine uniquely the isomorphism class of [Formula: see text].

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13

Jamal, Baraa M., and Ali Alabdali. "Nonabelian Case of Hopf Galois Structures on Nonnormal Extensions of Degree pqw." European Journal of Pure and Applied Mathematics 16, no. 2 (2023): 1118–27. http://dx.doi.org/10.29020/nybg.ejpam.v16i2.4755.

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We look at Hopf Galois structures with square free pqw degree on separable field extensions (nonnormal) L/K. Where E/K is the normal closure of L/K, the group permutation of degree pqw is G = Gal(E/K). We study details of the nonabelian case, where Jl = ⟨σ, [τ, αl ]⟩ is a nonabelian regular subgroup of Hol(N) for 1 ≤ l ≤ w − 1. We first find the group permutation G, and then the Hopf Galois structures for each G. In this case, there exists four G such that the Hopf Galois structures are admissible within the field extensions L/K.

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14

BALACHANDRAN, A. P., A. DAUGHTON, Z. C. GU, G. MARMO, R. D. SORKIN, and A. M. SRIVASTAVA. "A TOPOLOGICAL SPIN-STATISTICS THEOREM OR A USE OF THE ANTIPARTICLE." Modern Physics Letters A 05, no. 20 (1990): 1575–85. http://dx.doi.org/10.1142/s0217732390001797.

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A spin-statistics theorem for spinning particles in ℝd is proved without using relativity or field theory, but assuming the existence of antiparticles. The theorem excludes non-abelian statistics such as parastatistics of order 2 and more for d≥3 and statistics based on nonabelian representations of the braid groups for d=2.

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15

Jarlskog, Cecilia. "Supersymmetry: Early Roots That Did Not Grow." Advances in High Energy Physics 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/764875.

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This paper is about early roots of supersymmetry, as found in the literature from 1940s and early 1950s. There were models where the power of “partners” in alleviating divergences in quantum field theory was recognized. However, other currently known remarkable features of supersymmetry, such as its role in the extension of the Poincaré group, were not known. There were, of course, no supersymmetric nonabelian quantum field theories in those days.

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16

Rota, Gian-Carlo. "Class field theory." Advances in Mathematics 62, no. 1 (1986): 102. http://dx.doi.org/10.1016/0001-8708(86)90094-0.

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17

Florio, Giuseppe. "Decoherence in Holonomic Quantum Computation." Open Systems & Information Dynamics 13, no. 03 (2006): 263–72. http://dx.doi.org/10.1007/s11080-006-9006-2.

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Geometric phases are an interesting field of research in quantum mechanics. Recently both abelian and nonabelian geometric phases have been proposed as a useful resource for the experimental implementation of quantum computation. In this paper we focus on a particular physical model and study the effect of a bosonic bath on a class of holonomic transformations. We write a general master equation for time-dependent Hamiltonians and derive analytical and numerical solutions for the system considered. The fidelity is analyzed in the adiabatic and nonadiabatic regime. We also determine an optimal

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18

Hartl, Manfred. "The Nonabelian Tensor Square and Schur Multiplicator of Nilpotent Groups of Class 2." Journal of Algebra 179, no. 2 (1996): 416–40. http://dx.doi.org/10.1006/jabr.1996.0018.

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19

Tae Kim, Won, and Young-Jai Park. "Batalin-Tyutin quantization of the (2+1) dimensional nonabelian Chern-Simons field theory." Physics Letters B 336, no. 3-4 (1994): 376–80. http://dx.doi.org/10.1016/0370-2693(94)90548-7.

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20

LINK, ROBERT. "PHASE HOLONOMY OF THE VACUUM IN THREE-DIMENSIONAL GAUGE THEORIES." International Journal of Modern Physics A 07, no. 20 (1992): 4937–48. http://dx.doi.org/10.1142/s0217751x92002234.

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The phase two-form of Berry in the neighborhood of a degeneracy of the Fock vacuum of a semisimple, nonabelian, second-quantized, relativistic fermion-background gauge field Hamiltonian is shown to be that of the Dirac magnetic monopole—thus extending a result of Berry to field theory. The Dirac Hamiltonian for an SU(2) fermion on the two-sphere is solved in a particular two-parameter family of background instanton gauge potentials as an explicit illustrative example.

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21

CASTRO PERELMAN, CARLOS. "THE EXCEPTIONAL E8 GEOMETRY OF CLIFFORD (16) SUPERSPACE AND CONFORMAL GRAVITY YANG–MILLS GRAND UNIFICATION." International Journal of Geometric Methods in Modern Physics 06, no. 03 (2009): 385–417. http://dx.doi.org/10.1142/s0219887809003588.

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We continue to study the Chern–Simons E8 Gauge theory of Gravity developed by the author which is a unified field theory (at the Planck scale) of a Lanczos–Lovelock Gravitational theory with a E8 Generalized Yang–Mills (GYM) field theory, and is defined in the 15D boundary of a 16D bulk space. The Exceptional E8 Geometry of the 256-dim slice of the 256 × 256-dimensional flat Clifford (16) space is explicitly constructed based on a spin connection [Formula: see text], that gauges the generalized Lorentz transformations in the tangent space of the 256-dim curved slice, and the 256 × 256 componen

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22

Ayyer, Arvind, Anne Schilling, Benjamin Steinberg, and Nicolas M. Thiéry. "Markov chains, ${\mathscr R}$-trivial monoids and representation theory." International Journal of Algebra and Computation 25, no. 01n02 (2015): 169–231. http://dx.doi.org/10.1142/s0218196715400081.

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We develop a general theory of Markov chains realizable as random walks on [Formula: see text]-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via Möbius inversion along a lattice, a condition for diagonalizability of the transition matrix and some techniques for bounding the mixing time. In addition, we discuss several examples, such as Toom–Tsetlin models, an exchange walk for finite Coxeter groups, as well as examples previously studied by the authors, such as nonabelian sandpile models and the pro

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23

PELLING, SIMON, and ALICE ROGERS. "MULTISYMPLECTIC BRST." International Journal of Geometric Methods in Modern Physics 10, no. 08 (2013): 1360012. http://dx.doi.org/10.1142/s0219887813600128.

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After briefly describing Hamiltonian BRST methods and the multisymplectic approach to field theory, a symmetric geometric Lagrangian is studied by extending the BRST method to the multisymplectic setting. This work uses ideas first introduced by Hrabak [On the multisymplectic origin of the nonabelian deformation algebra of pseudoholomorphic embeddings in strictly almost Kähler ambient manifolds, and the corresponding BRST algebra, preprint (1999), arXiv: math-ph/9904026].

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24

MORENO, MATÍAS, RODOLFO MARTÍNEZ, and ARTURO ZENTELLA. "SUPERSYMMETRY, FOLDY-WOUTHUYSEN TRANSFORMATION AND STABILITY OF THE DIRAC SEA." Modern Physics Letters A 05, no. 12 (1990): 949–54. http://dx.doi.org/10.1142/s0217732390001050.

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It is shown that for a large class of potential problems in the Dirac equation the positive and negative energy solutions do not mix even in the strong coupling limit We prove that this property, which implies a stability of the Dirac sea, is connected to the presence of superalgebra operators in the Dirac equation. The exact and closed form for the Foldy-Wouthuysen Hamiltonian which is used to prove this property are given. The potentials include the Dirac oscillator, the uniform time-independent magnetic field and the odd potentials and its nonabelian generalizations.

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25

Ershov, Yu L. "Local class field theory." St. Petersburg Mathematical Journal 15, no. 06 (2004): 837–47. http://dx.doi.org/10.1090/s1061-0022-04-00834-9.

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26

Feng, Tony, Michael Harris, and Barry Mazur. "Derived class field theory." Notices of the International Consortium of Chinese Mathematicians 11, no. 2 (2023): 88–98. http://dx.doi.org/10.4310/iccm.2023.v11.n2.a10.

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27

Heidenreich, Ben, Matthew Reece, and Tom Rudelius. "Axion experiments to algebraic geometry: Testing quantum gravity via the Weak Gravity Conjecture." International Journal of Modern Physics D 25, no. 12 (2016): 1643005. http://dx.doi.org/10.1142/s0218271816430057.

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Common features of known quantum gravity theories may hint at the general nature of quantum gravity. The absence of continuous global symmetries is one such feature. This inspired the Weak Gravity Conjecture, which bounds masses of charged particles. We propose the Lattice Weak Gravity Conjecture, which further requires the existence of an infinite tower of particles of all possible charges under both abelian and nonabelian gauge groups and directly implies a cutoff for quantum field theory. It holds in a wide variety of string theory examples and has testable consequences for the real world a

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28

Shau, Moumita, and Fernando Szechtman. "Clifford theory of Weil representations of unitary groups." Journal of Group Theory 22, no. 6 (2019): 975–99. http://dx.doi.org/10.1515/jgth-2018-0151.

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Abstract Let {\mathcal{O}} be an involutive discrete valuation ring with residue field of characteristic not 2. Let A be a quotient of {\mathcal{O}} by a nonzero power of its maximal ideal, and let {*} be the involution that A inherits from {\mathcal{O}} . We consider various unitary groups {\mathcal{U}_{m}(A)} of rank m over A, depending on the nature of {*} and the equivalence type of the underlying hermitian or skew hermitian form. Each group {\mathcal{U}_{m}(A)} gives rise to a Weil representation. In this paper, we give a Clifford theory description of all irreducible components of the We

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29

WRIGHT, GRETCHEN. "THE RESHETIKHIN-TURAEV REPRESENTATION OF THE MAPPING CLASS GROUP AT THE SIXTH ROOT OF UNITY." Journal of Knot Theory and Its Ramifications 05, no. 05 (1996): 721–39. http://dx.doi.org/10.1142/s0218216596000412.

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The quantum group construction of Reshetikhin and Turaev provides representations of the mapping class group, indexed by an integer parameter r. This paper presents computations of these representations when r=6, and analyzes their relationship to other topological invariants. It is shown that in genus 2, the representation splits into two summands. The first summand factors through the mapping class group action on the first homology of the surface with Z/3Z coefficients, while the second summand can be analyzed via its restriction to the subgroup of the mapping class group which is normally

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30

VALERIOTE, MATTHEW A., and ROSS WILLARD. "SOME PROPERTIES OF FINITELY DECIDABLE VARIETIES." International Journal of Algebra and Computation 02, no. 01 (1992): 89–101. http://dx.doi.org/10.1142/s0218196792000074.

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Let [Formula: see text] be a variety whose class of finite members has a decidable first-order theory. We prove that each finite member A of [Formula: see text] satisfies the (3, 1) and (3, 2) transfer principles, and that the minimal sets of prime quotients of type 2 or 3 in A must have empty tails. The first result has already been used by J. Jeong [9] in characterizing the finite subdirectly irreducible members of [Formula: see text] with nonabelian monolith. The second result implies that if [Formula: see text] is also locally finite and omits type 1, then [Formula: see text] is congruence

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31

Stumpf, H. "Composite Gluons and Effective Nonabelian Gluon Dynamics in a Unified Spinor-Isospinor Preon Field Model." Zeitschrift für Naturforschung A 42, no. 3 (1987): 213–26. http://dx.doi.org/10.1515/zna-1987-0301.

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The model is defined by a selfregularizing nonlinear preon field equation and all observable (elementary and non-elementary) particles are assumed to be bound (quantum) states of the fermionic preon fields. In particular electroweak gauge bosons are two-particle composites, leptons and quarks are three-particle composites, and gluons are six-particle composites. Electroweak gauge bosons, leptons and quarks and their effective interactions etc. were studied in preceding papers. In this paper gluons and their effective dynamics are discussed. Due to the complications of a six-particle bound stat

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32

Jusoo, Siti Hasanah, Mohd Sham Mohamad, Sahimel Azwal Sulaiman, and Faisal. "Some analysis on conjugacy search problem for Diffie-Hellman protocol." Data Analytics and Applied Mathematics (DAAM) 3, no. 2 (2022): 13–17. http://dx.doi.org/10.15282/daam.v3i2.8936.

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The field in nonabelian group-based cryptosystem have gain attention of the researchers as it expected to offers higher security when confronted with quantum computational due to more complex algebraic structures. Hence, this paper intents to give an overview on Diffie-Hellman protocol considering the mathematically hard problem such as the conjugacy search problem in a group G. In this paper we provide examples for G of non abelian group particularly the group of SL(2,3).

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33

Koch, Helmut, Susanne Kukkuk, and John Labute. "Nilpotent local class field theory." Acta Arithmetica 83, no. 1 (1998): 45–64. http://dx.doi.org/10.4064/aa-83-1-45-64.

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34

Hazewinkel, Michiel. "Book Review: Class field theory." Bulletin of the American Mathematical Society 21, no. 1 (1989): 95–102. http://dx.doi.org/10.1090/s0273-0979-1989-15772-8.

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35

Fesenko, Ivan B. "Abelian localp-class field theory." Mathematische Annalen 301, no. 1 (1995): 561–86. http://dx.doi.org/10.1007/bf01446646.

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36

Nair, V. P. "Sasakians and the geometry of a mass term." Reviews in Mathematical Physics 33, no. 08 (2021): 2140002. http://dx.doi.org/10.1142/s0129055x2140002x.

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A gauge-invariant mass term for nonabelian gauge fields in two dimensions can be expressed as the Wess–Zumino–Witten (WZW) action. Hard thermal loops in the gauge theory in four dimensions at finite temperatures generate a screening mass for some components of the gauge field. This can be expressed in terms of the WZW action using the bundle of complex structures (for Euclidean signature) or the bundle of lightcones over Minkowski space. We show that a dynamically generated mass term in three dimensions can be put within the same general framework using the bundle of Sasakian structures.

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37

Yoshida, Teruyoshi. "Local Class Field Theory via Lubin-Tate Theory." Annales de la faculté des sciences de Toulouse Mathématiques 17, no. 2 (2008): 411–38. http://dx.doi.org/10.5802/afst.1188.

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38

Fesenko, Ivan B. "LOCAL CLASS FIELD THEORY: PERFECT RESIDUE FIELD CASE." Russian Academy of Sciences. Izvestiya Mathematics 43, no. 1 (1994): 65–81. http://dx.doi.org/10.1070/im1994v043n01abeh001559.

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39

Kim, Junhyeung, Hisatoshi Kodani, and Masanori Morishita. "Nilpotent class field theory for manifolds." Proceedings of the Japan Academy, Series A, Mathematical Sciences 89, no. 1 (2013): 15–19. http://dx.doi.org/10.3792/pjaa.89.15.

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40

Stevenhagen, Peter. "Unramified class field theory for orders." Transactions of the American Mathematical Society 311, no. 2 (1989): 483. http://dx.doi.org/10.1090/s0002-9947-1989-0978366-3.

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41

KERZ, MORITZ, and YIGENG ZHAO. "HIGHER IDELES AND CLASS FIELD THEORY." Nagoya Mathematical Journal 236 (October 2, 2018): 214–50. http://dx.doi.org/10.1017/nmj.2018.34.

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42

Iovita, Adrian, and Alexandru Zaharescu. "Nondiscrete local ramified class field theory." Journal of Mathematics of Kyoto University 35, no. 2 (1995): 325–39. http://dx.doi.org/10.1215/kjm/1250518774.

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43

Titan, Qingchun. "Class Field Theory for Arithmetic Surfaces." K-Theory 13, no. 2 (1998): 123–49. http://dx.doi.org/10.1023/a:1007722903192.

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44

Wiesend, Götz. "Class field theory for arithmetic schemes." Mathematische Zeitschrift 256, no. 4 (2007): 717–29. http://dx.doi.org/10.1007/s00209-006-0095-y.

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45

Spiess, Michael. "Class Formations and Higher Dimensional Local Class Field Theory." Journal of Number Theory 62, no. 2 (1997): 273–83. http://dx.doi.org/10.1006/jnth.1997.2048.

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46

Ikeda, Kâzim Ilhan, and Erol Serbest. "Ramification theory in non-abelian local class field theory." Acta Arithmetica 144, no. 4 (2010): 373–93. http://dx.doi.org/10.4064/aa144-4-4.

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47

Hansson, J. "A simple explanation of the nonappearance of physical gluons and quarks." Canadian Journal of Physics 80, no. 9 (2002): 1093–97. http://dx.doi.org/10.1139/p02-034.

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We show that the nonappearance of gluons and quarks as physical particles is a rigorous and automatic result of the full, i.e., nonperturbative, nonabelian nature of the color interaction in quantum chromodynamics (QCD). This makes it, in general, impossible to describe the color field as a collection of elementary quanta (gluons). Neither can a quark be an elementary quantum of the quark field, as the color field of which it is the source is itself a source, making isolated noninteracting quarks, crucial for a physical particle interpretation, impossible. In geometrical language, the impossib

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48

NIIBO, Hirofumi. "IDÈLIC CLASS FIELD THEORY FOR 3-MANIFOLDS." Kyushu Journal of Mathematics 68, no. 2 (2014): 421–36. http://dx.doi.org/10.2206/kyushujm.68.421.

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49

Saito, Shuji. "Unramified Class Field Theory of Arithmetical Schemes." Annals of Mathematics 121, no. 2 (1985): 251. http://dx.doi.org/10.2307/1971173.

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50

Cohen, Henri. "A survey of computational class field theory." Journal de Théorie des Nombres de Bordeaux 11, no. 1 (1999): 1–13. http://dx.doi.org/10.5802/jtnb.235.

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