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Journal articles on the topic 'Lie group'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2025

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1

Merati, S., and M. R. Farhangdoost. "Hom-Lie group and hom-Lie algebra from Lie group and Lie algebra perspective." International Journal of Geometric Methods in Modern Physics 18, no. 05 (January 29, 2021): 2150068. http://dx.doi.org/10.1142/s0219887821500687.

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A hom-Lie group structure is a smooth group-like multiplication on a manifold, where the structure is twisted by a isomorphism. The notion of hom-Lie group was introduced by Jiang et al. as integration of hom-Lie algebra. In this paper we want to study hom-Lie group and hom-Lie algebra from the Lie group’s point of view. We show that some of important hom-Lie group issues are equal to similar types in Lie groups and then many of these issues can be studied by Lie group theory.

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2

Iserles, Arieh, Hans Z. Munthe-Kaas, Syvert P. Nørsett, and Antonella Zanna. "Lie-group methods." Acta Numerica 9 (January 2000): 215–365. http://dx.doi.org/10.1017/s0962492900002154.

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Many differential equations of practical interest evolve on Lie groups or on manifolds acted upon by Lie groups. The retention of Lie-group structure under discretization is often vital in the recovery of qualitatively correct geometry and dynamics and in the minimization of numerical error. Having introduced requisite elements of differential geometry, this paper surveys the novel theory of numerical integrators that respect Lie-group structure, highlighting theory, algorithmic issues and a number of applications.

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3

Pham, David N. "On the tangent Lie group of a symplectic Lie group." Ricerche di Matematica 68, no. 2 (January 29, 2019): 699–704. http://dx.doi.org/10.1007/s11587-019-00434-2.

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4

Rybicki, Tomasz. "A Lie group structure on strict groups." Publicationes Mathematicae Debrecen 61, no. 3-4 (October 1, 2002): 533–48. http://dx.doi.org/10.5486/pmd.2002.2670.

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5

Shtern, A. I. "Connected Lie Groups Admitting an Embedding in a Connected Amenable Lie Group." Russian Journal of Mathematical Physics 26, no. 4 (October 2019): 499–500. http://dx.doi.org/10.1134/s1061920819040083.

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6

Lichnerowicz, Andr�. "Characterization of Lie groups on the cotangent bundle of a Lie group." Letters in Mathematical Physics 12, no. 2 (August 1986): 111–21. http://dx.doi.org/10.1007/bf00416461.

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7

Khalili, Valiollah. "On the structure of graded 3-Lie-Rinehart algebras." Filomat 38, no. 2 (2024): 369–92. http://dx.doi.org/10.2298/fil2402369k.

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We study the structure of a graded 3-Lie-Rinehart algebraLover an associative and commutative graded algebra A. For G an abelian group, we show that if (L,A) is a tight G-graded 3-Lie-Rinehart algebra, then L and A decompose as L = ? i?I Li and A = ? j?J Aj, where any Li is a non-zero graded ideal of L satisfying [Li1 ,Li2 ,Li3] = 0 for any i1, i2, i3 ? I different from each other, and any Aj is a non-zero graded ideal of A satisfying AjAl = 0 for any l, j ? J such that j ?l, and both decompositions satisfy that for any i ? I there exists a unique j ? J such that AjLi ? 0. Furthermore, any (Li,Aj) is a graded 3-Lie-Rinehart algebra. Also, under certain conditions, it is shown that the above decompositions of L and A are by means of the family of their, respectively, graded simple ideals.

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8

Glöckner, Helge. "Lie Group Structures on Quotient Groups and Universal Complexifications for Infinite-Dimensional Lie Groups." Journal of Functional Analysis 194, no. 2 (October 2002): 347–409. http://dx.doi.org/10.1006/jfan.2002.3942.

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9

Cárdenas, Cristian Camilo, and Ivan Struchiner. "Stability of Lie group homomorphisms and Lie subgroups." Journal of Pure and Applied Algebra 224, no. 3 (March 2020): 1280–96. http://dx.doi.org/10.1016/j.jpaa.2019.07.017.

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10

Kamber, Franz W., and Peter W. Michor. "Completing Lie algebra actions to Lie group actions." Electronic Research Announcements of the American Mathematical Society 10, no. 1 (February 18, 2004): 1–10. http://dx.doi.org/10.1090/s1079-6762-04-00124-6.

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11

Lesimple, Marc, and Georges Pinczon. "Deformations of Lie group and Lie algebra representations." Journal of Mathematical Physics 34, no. 9 (September 1993): 4251–72. http://dx.doi.org/10.1063/1.529998.

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12

Benedetto, Elmo. "Lie Group of Spacetime." ISRN Astronomy and Astrophysics 2011 (April 10, 2011): 1–7. http://dx.doi.org/10.5402/2011/873830.

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A brief review is presented of de Sitter-Fantappiè relativity, and we propose some cosmological reflections suggested by this theory. Compared to the original works, some deductions have been very simplified, and only the physical meaning of the equations has been analyzed.

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13

Malham, Simon J. A., and Anke Wiese. "Stochastic Lie Group Integrators." SIAM Journal on Scientific Computing 30, no. 2 (January 2008): 597–617. http://dx.doi.org/10.1137/060666743.

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14

Poguntke, D. "Dense Lie Group Homomorphisms." Journal of Algebra 169, no. 2 (October 1994): 625–47. http://dx.doi.org/10.1006/jabr.1994.1300.

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15

Miah, Md Shapan, Khondokar M. Ahmed, and Salma Nasrin. "Characteristics of General Linear Group of Order 2 as Lie Group and Lie Algebra." Dhaka University Journal of Science 71, no. 1 (May 29, 2023): 82–86. http://dx.doi.org/10.3329/dujs.v71i1.65277.

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The main target of this article is to study about Lie Groups, Lie Algebras. This article will enrich our knowledge about Algebraic properties of manifolds, how Lie Groups and Lie Algebras are working with their properties. Finally, we have discussed an example by showing all the properties of Lie Algebra,Lie Groups for a special Group and a Theorem has established. Dhaka Univ. J. Sci. 71(1): 82-86, 2023 (Jan)

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16

ANDO, Hiroshi, and Yasumichi MATSUZAWA. "Lie group-Lie algebra correspondences of unitary groups in finite von Neumann algebras." Hokkaido Mathematical Journal 41, no. 1 (February 2012): 31–99. http://dx.doi.org/10.14492/hokmj/1330351338.

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17

Podoksenov, M. N., and G. Yang. "Complete group of isometries of the special three-dimensional Lie group." Mathematical structures and modeling, no. 3 (2024): 33–43. http://dx.doi.org/10.24147/2222-8772.2024.3.33-43.

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We consider a special three-dimensional Lie algebra 3 of Bianchi type V. A matrix representation of this Lie algebra and the corresponding connected simply connected Lie group 𝑆3 is found and natural coordinates are introduced, which are determined by the matrix representation. Formulas for exponential mapping with respect to natural coordinates are found. Complete groups of autoisometries of the special Lie algebra with respect to the Euclidean or Lorentz scalar product are written out. The leftinvariant Riemannian metric of the Lie group 𝑆3 and the complete group of isometries of the resulting homogeneous manifold are found. This manifold turned out to be a space of constant Ricci curvature.

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18

Knapp, A. W., Andrew Baker, and Wulf Rossmann. "Matrix Groups: An Introduction to Lie Group Theory." American Mathematical Monthly 110, no. 5 (May 2003): 446. http://dx.doi.org/10.2307/3647845.

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19

Mickelsson, Jouko, and Stefan Wagner. "Third group cohomology and gerbes over Lie groups." Journal of Geometry and Physics 108 (October 2016): 49–70. http://dx.doi.org/10.1016/j.geomphys.2016.06.015.

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20

Marin, Ivan. "Group Algebras of Finite Groups as Lie Algebras." Communications in Algebra 38, no. 7 (June 21, 2010): 2572–84. http://dx.doi.org/10.1080/00927870903417638.

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21

Zimmer, Robert J. "Groups generating transversals to semisimple lie group actions." Israel Journal of Mathematics 73, no. 2 (June 1991): 151–59. http://dx.doi.org/10.1007/bf02772946.

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22

Nagata, Yoshikazu. "On the Lie group structure of automorphism groups." Comptes Rendus Mathematique 355, no. 7 (July 2017): 769–73. http://dx.doi.org/10.1016/j.crma.2017.06.007.

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23

Wilking, Burkhard. "Rigidity of group actions on solvable Lie groups." Mathematische Annalen 317, no. 2 (June 1, 2000): 195–237. http://dx.doi.org/10.1007/s002089900091.

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24

HOFMANN, K. H., and K. H. NEEB. "Pro-Lie groups which are infinite-dimensional Lie groups." Mathematical Proceedings of the Cambridge Philosophical Society 146, no. 2 (March 2009): 351–78. http://dx.doi.org/10.1017/s030500410800128x.

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AbstractA pro-Lie group is a projective limit of a family of finite-dimensional Lie groups. In this paper we show that a pro-Lie group G is a Lie group in the sense that its topology is compatible with a smooth manifold structure for which the group operations are smooth if and only if G is locally contractible. We also characterize the corresponding pro-Lie algebras in various ways. Furthermore, we characterize those pro-Lie groups which are locally exponential, that is, they are Lie groups with a smooth exponential function which maps a zero neighbourhood in the Lie algebra diffeomorphically onto an open identity neighbourhood of the group.

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25

Catino, Francesco, and Ernesto Spinelli. "Lie Nilpotent Group Algebras and Upper Lie Codimension Subgroups." Communications in Algebra 34, no. 10 (October 2006): 3859–73. http://dx.doi.org/10.1080/00927870600862698.

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26

Schmeding, Alexander, and Christoph Wockel. "The Lie group of bisections of a Lie groupoid." Annals of Global Analysis and Geometry 48, no. 1 (April 11, 2015): 87–123. http://dx.doi.org/10.1007/s10455-015-9459-z.

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27

Bhatt, Suchi, and Harish Chandra. "A note on modular group algebras with upper Lie nilpotency indices." Algebra and Discrete Mathematics 33, no. 2 (2022): 1–20. http://dx.doi.org/10.12958/adm1694.

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Let KG be the modular group algebra of anarbitrary group G over a field K of characteristic p>0. In thispaper we give some improvements of upper Lie nilpotency indext L(KG) of the group algebra KG. It can be seen that if KG is Lie nilpotent, then its lower as well as upper Lie nilpotency index is atleast p+1. In this way the classification of group algebras KG with next upper Lie nilpotency indext L(KG) up to 9p−7 have alreadybeen classified. Furthermore, we give a complete classification ofmodular group algebraKGfor which the upper Lie nilpotency index is 10p−8.

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28

Hosseini, Arezoo, and Leila Mohamadnia. "Enlargement of A Local Group To A Group." JOURNAL OF ADVANCES IN MATHEMATICS 12, no. 11 (January 17, 2016): 6835–39. http://dx.doi.org/10.24297/jam.v12i11.359.

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Local lie groups are introduced by Cartan [1]. Local groups are local lie groups without topologically property. The aim of this paper is to find conditions that a local group is contained in a group . It is showed in the example 3.2 that every local groups is not gllobaly associative . Then it may not be extended to a group.

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29

Oğuz, Gülay, Ilhan Içen, and Gürsoy Habil. "Lie rough groups." Filomat 32, no. 16 (2018): 5735–41. http://dx.doi.org/10.2298/fil1816735o.

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This paper introduces the definition of a Lie rough group as a natural development of the concepts of a smooth manifold and a rough group on an approximation space. Furthermore, the properties of Lie rough groups are discussed. It is shown that every Lie rough group is a topological rough group, and that the product of two Lie rough groups is again a Lie rough group. We define the concepts of Lie rough subgroups and Lie rough normal subgroups. Finally, our aim is to give an example by using definition of Lie rough homomorphism sets G and H.

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30

Senashov, S. I., and I. L. Savostyanova. "Hook’s law as Lie group." IOP Conference Series: Materials Science and Engineering 822 (May 22, 2020): 012031. http://dx.doi.org/10.1088/1757-899x/822/1/012031.

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31

Giambruno, Antonio, and Sudarshan K. Sehgal. "Lie nilpotence of group rings." Communications in Algebra 21, no. 11 (January 1993): 4253–61. http://dx.doi.org/10.1080/00927879308824797.

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32

Gao, Yanyan. "Lie *-Nilpotence of Group Rings." Communications in Algebra 42, no. 7 (March 13, 2014): 2800–2812. http://dx.doi.org/10.1080/00927872.2013.820737.

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33

Ha, Yuan K. "Bosonization and Lie Group Structure." Journal of Physics: Conference Series 563 (November 26, 2014): 012013. http://dx.doi.org/10.1088/1742-6596/563/1/012013.

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34

Aldaya, V., and J. Guerrero. "Lie group representations and quantization." Reports on Mathematical Physics 47, no. 2 (April 2001): 213–40. http://dx.doi.org/10.1016/s0034-4877(01)80038-0.

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35

Celledoni, Elena, Arne Marthinsen, and Brynjulf Owren. "Commutator-free Lie group methods." Future Generation Computer Systems 19, no. 3 (April 2003): 341–52. http://dx.doi.org/10.1016/s0167-739x(02)00161-9.

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36

Inaba, Takashi, Shigenori Matsumoto, and Yoshihiko Mitsumatsu. "Normally contracting Lie group actions." Topology and its Applications 159, no. 5 (March 2012): 1334–38. http://dx.doi.org/10.1016/j.topol.2011.12.012.

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37

Levin, Frank, and Gerhard Rosenberger. "On Lie metabelian group rings." Results in Mathematics 26, no. 1-2 (August 1994): 83–88. http://dx.doi.org/10.1007/bf03322289.

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38

Trouvé, Alain, and Laurent Younes. "Metamorphoses Through Lie Group Action." Foundations of Computational Mathematics 5, no. 2 (February 11, 2005): 173–98. http://dx.doi.org/10.1007/s10208-004-0128-z.

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39

Hall, James, and Melvin Leok. "Lie Group Spectral Variational Integrators." Foundations of Computational Mathematics 17, no. 1 (November 11, 2015): 199–257. http://dx.doi.org/10.1007/s10208-015-9287-3.

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40

Sharma, R. K., and J. B. Srivastava. "Lie centrally metabelian group rings." Journal of Algebra 151, no. 2 (October 1992): 476–86. http://dx.doi.org/10.1016/0021-8693(92)90123-4.

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41

Forest, Étienne. "Sixth-order lie group integrators." Journal of Computational Physics 98, no. 2 (February 1992): 349. http://dx.doi.org/10.1016/0021-9991(92)90162-r.

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42

Forest, Étienne. "Sixth-order lie group integrators." Journal of Computational Physics 99, no. 2 (April 1992): 209–13. http://dx.doi.org/10.1016/0021-9991(92)90203-b.

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43

Alekseev, Anton, Anton Malkin, and Eckhard Meinrenken. "Lie group valued moment maps." Journal of Differential Geometry 48, no. 3 (1998): 445–95. http://dx.doi.org/10.4310/jdg/1214460860.

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44

Bovdi, A. A., and I. I. Khripta. "GENERALIZED LIE NILPOTENT GROUP RINGS." Mathematics of the USSR-Sbornik 57, no. 1 (February 28, 1987): 165–69. http://dx.doi.org/10.1070/sm1987v057n01abeh003061.

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45

Boya, Luis J. "Problems in Lie group theory." Journal of Optics B: Quantum and Semiclassical Optics 5, no. 3 (June 1, 2003): S261—S265. http://dx.doi.org/10.1088/1464-4266/5/3/356.

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46

Klein, Nadav, and Nicholas Epley. "Group discussion improves lie detection." Proceedings of the National Academy of Sciences 112, no. 24 (May 26, 2015): 7460–65. http://dx.doi.org/10.1073/pnas.1504048112.

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Groups of individuals can sometimes make more accurate judgments than the average individual could make alone. We tested whether this group advantage extends to lie detection, an exceptionally challenging judgment with accuracy rates rarely exceeding chance. In four experiments, we find that groups are consistently more accurate than individuals in distinguishing truths from lies, an effect that comes primarily from an increased ability to correctly identify when a person is lying. These experiments demonstrate that the group advantage in lie detection comes through the process of group discussion, and is not a product of aggregating individual opinions (a “wisdom-of-crowds” effect) or of altering response biases (such as reducing the “truth bias”). Interventions to improve lie detection typically focus on improving individual judgment, a costly and generally ineffective endeavor. Our findings suggest a cheap and simple synergistic approach of enabling group discussion before rendering a judgment.

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47

Giambruno, A., C. Polcino Milies, and Sudarshan K. Sehgal. "Group algebras and Lie nilpotence." Journal of Algebra 373 (January 2013): 276–83. http://dx.doi.org/10.1016/j.jalgebra.2012.09.043.

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48

Levin, Frank, and Sudarshan Sehgal. "On lie nilpotent group rings." Journal of Pure and Applied Algebra 37 (1985): 33–39. http://dx.doi.org/10.1016/0022-4049(85)90085-4.

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49

Bhandari, A. K., and I. B. S. Passi. "Residually Lie nilpotent group rings." Archiv der Mathematik 58, no. 1 (January 1992): 1–6. http://dx.doi.org/10.1007/bf01198635.

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50

Curry, Charles, and Alexander Schmeding. "Convergence of Lie group integrators." Numerische Mathematik 144, no. 2 (October 30, 2019): 357–73. http://dx.doi.org/10.1007/s00211-019-01083-1.

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