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Journal articles on the topic 'Lie groups'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Hiraga, Kaoru. "Lie groups." Duke Mathematical Journal 85, no. 1 (1996): 167–81. http://dx.doi.org/10.1215/s0012-7094-96-08507-5.

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2

Alekseevskii, D. V. "Lie groups." Journal of Soviet Mathematics 28, no. 6 (1985): 924–49. http://dx.doi.org/10.1007/bf02105458.

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3

Ni, Xiang, and Chengming Bai. "Special symplectic Lie groups and hypersymplectic Lie groups." manuscripta mathematica 133, no. 3-4 (2010): 373–408. http://dx.doi.org/10.1007/s00229-010-0375-z.

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4

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 (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

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5

Wüstner, Michael. "Splittable Lie Groups and Lie Algebras." Journal of Algebra 226, no. 1 (2000): 202–15. http://dx.doi.org/10.1006/jabr.1999.8162.

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6

Fioresi, Rita, and Robert Yuncken. "Quantized semisimple Lie groups." Archivum Mathematicum, no. 5 (2024): 311–49. https://doi.org/10.5817/am2024-5-311.

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7

Hofmann, Karl H., Sidney A. Morris, and Markus Stroppel. "Locally compact groups, residual Lie groups, and varieties generated by Lie groups." Topology and its Applications 71, no. 1 (1996): 63–91. http://dx.doi.org/10.1016/0166-8641(95)00068-2.

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8

Howard, Eric. "Theory of groups and symmetries: Finite groups, Lie groups and Lie algebras." Contemporary Physics 60, no. 3 (2019): 275. http://dx.doi.org/10.1080/00107514.2019.1663933.

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9

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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10

Pressley, Andrew N. "LIE GROUPS AND ALGEBRAIC GROUPS." Bulletin of the London Mathematical Society 23, no. 6 (1991): 612–14. http://dx.doi.org/10.1112/blms/23.6.612b.

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11

Wojtyński, Wojciech. "Lie groups as quotient groups." Reports on Mathematical Physics 40, no. 2 (1997): 373–79. http://dx.doi.org/10.1016/s0034-4877(97)85935-6.

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12

Doran, C., D. Hestenes, F. Sommen, and N. Van Acker. "Lie groups as spin groups." Journal of Mathematical Physics 34, no. 8 (1993): 3642–69. http://dx.doi.org/10.1063/1.530050.

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13

Moller, Jesper M. "Homotopy Lie Groups." Bulletin of the American Mathematical Society 32, no. 4 (1995): 413–29. http://dx.doi.org/10.1090/s0273-0979-1995-00613-0.

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14

Bagley, R. W., T. S. Wu, and J. S. Yang. "Pro-Lie groups." Transactions of the American Mathematical Society 287, no. 2 (1985): 829. http://dx.doi.org/10.1090/s0002-9947-1985-0768744-6.

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15

MARQUIS, T., and K.-H. NEEB. "HALF-LIE GROUPS." Transformation Groups 23, no. 3 (2018): 801–40. http://dx.doi.org/10.1007/s00031-018-9485-6.

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16

Li-Bland, David, and Eckhard Meinrenken. "Dirac Lie groups." Asian Journal of Mathematics 18, no. 5 (2014): 779–816. http://dx.doi.org/10.4310/ajm.2014.v18.n5.a2.

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17

Virg�s, Enrique Macias. "Non-closed Lie subgroups of Lie groups." Annals of Global Analysis and Geometry 11, no. 1 (1993): 35–40. http://dx.doi.org/10.1007/bf00773362.

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18

Alioune, Brahim, Mohamed Boucetta, and Ahmed Sid’Ahmed Lessiad. "On Riemann-Poisson Lie groups." Archivum Mathematicum, no. 4 (2020): 225–47. http://dx.doi.org/10.5817/am2020-4-225.

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19

Bucki, Andrew. "Para-f-Lie groups." International Journal of Mathematics and Mathematical Sciences 2003, no. 49 (2003): 3149–52. http://dx.doi.org/10.1155/s0161171203211273.

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Special para-f-structures on Lie groups are studied. It is shown that every para-f-Lie groupGis the quotient of the product of an almost product Lie group and a Lie group with trivial para-f-structure by a discrete subgroup.

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20

SATOH, TAKAO. "On the basis-conjugating automorphism groups of free groups and free metabelian groups." Mathematical Proceedings of the Cambridge Philosophical Society 158, no. 1 (2014): 83–109. http://dx.doi.org/10.1017/s0305004114000619.

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AbstractIn this paper we study the images of the Johnson homomorphisms of the basis-conjugating automorphism groups of free groups and free metabelian groups. In particular, we show that the Johnson image is contained in a certain proper Lie subalgebra $\mathfrak{p}$Mn of the derivation algebra of the Chen Lie algebra. Furthermore, we completely determine the Johnson images, and give the abelianisation of $\mathfrak{p}$Mn as a Lie algebra by using Morita's trace maps.

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21

Lord, Nick, and N. Bourbaki. "Lie Groups and Lie Algebras (Chapters 1-3)." Mathematical Gazette 74, no. 468 (1990): 199. http://dx.doi.org/10.2307/3619408.

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22

Mikami, Kentaro, and Fumio Narita. "Dual Lie algebras of Heisenberg Poisson Lie groups." Tsukuba Journal of Mathematics 17, no. 2 (1993): 429–41. http://dx.doi.org/10.21099/tkbjm/1496162270.

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23

Chi, Kieu Phuong, Nguyen Huu Quang, and Bui Cao Van. "The Lie derivative of currents on Lie groups." Lobachevskii Journal of Mathematics 33, no. 1 (2012): 10–21. http://dx.doi.org/10.1134/s1995080212010027.

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24

Hilgert, Joachim, and Karl H. Hofmann. "Semigroups in Lie groups, semialgebras in Lie algebras." Transactions of the American Mathematical Society 288, no. 2 (1985): 481. http://dx.doi.org/10.1090/s0002-9947-1985-0776389-7.

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25

Ginzburg, Viktor L., and Alan Weinstein. "Lie-Poisson structure on some Poisson Lie groups." Journal of the American Mathematical Society 5, no. 2 (1992): 445. http://dx.doi.org/10.1090/s0894-0347-1992-1126117-8.

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26

Ruppert, Wolfgang A. F., and Brigitte E. Breckner. "On Lie semigroup analogues of parabolic Lie groups." Semigroup Forum 77, no. 1 (2008): 86–100. http://dx.doi.org/10.1007/s00233-008-9067-3.

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27

Cohen, Arjeh M., and Robert L. Griess. "Non-Local Lie Primitive Subgroups of Lie Groups." Canadian Journal of Mathematics 45, no. 1 (1993): 88–103. http://dx.doi.org/10.4153/cjm-1993-005-7.

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AbstractBorovik found a Lie primitive subgroup of E8(ℂ) isomorphic to (Alt5 × Sym6) : 2. In this note, we provide a short proof of existence and his result that the conjugacy class of this subgroup is the only one among those of non-local Lie primitive subgroups of finite dimensional simple complex Lie groups having a socle with more than one simple factor.

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28

Berenstein, Arkady, and Vladimir Retakh. "Lie algebras and Lie groups over noncommutative rings." Advances in Mathematics 218, no. 6 (2008): 1723–58. http://dx.doi.org/10.1016/j.aim.2008.03.003.

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29

Hanusch, Maximilian. "Regularity of Lie groups." Communications in Analysis and Geometry 30, no. 1 (2022): 53–152. http://dx.doi.org/10.4310/cag.2022.v30.n1.a2.

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30

Hasić, Amor. "Representations of Lie Groups." Advances in Linear Algebra & Matrix Theory 11, no. 04 (2021): 117–34. http://dx.doi.org/10.4236/alamt.2021.114009.

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31

Marthinsen, Arne. "Interpolation in Lie Groups." SIAM Journal on Numerical Analysis 37, no. 1 (1999): 269–85. http://dx.doi.org/10.1137/s0036142998338861.

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32

Landsberg, J. M., and L. Manivel. "Series of Lie groups." Michigan Mathematical Journal 52, no. 2 (2004): 453–79. http://dx.doi.org/10.1307/mmj/1091112085.

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33

Matumoto, Hisayosi. "split semisimple Lie groups." Duke Mathematical Journal 53, no. 3 (1986): 635–76. http://dx.doi.org/10.1215/s0012-7094-86-05335-4.

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34

Stembridge, John R. "in complex Lie groups." Duke Mathematical Journal 73, no. 2 (1994): 469–90. http://dx.doi.org/10.1215/s0012-7094-94-07320-1.

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35

Goetze, Edward R., and Ralf J. Spatzier. "of semisimple Lie groups." Duke Mathematical Journal 88, no. 1 (1997): 1–27. http://dx.doi.org/10.1215/s0012-7094-97-08801-3.

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36

Calvaruso, Giovanni, and Marco Castrillón López. "Cyclic Lorentzian Lie groups." Geometriae Dedicata 181, no. 1 (2015): 119–36. http://dx.doi.org/10.1007/s10711-015-0116-2.

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37

Golubchik, I. Z., and A. I. Murseeva. "Homomorphisms of Lie Groups." Journal of Mathematical Sciences 233, no. 5 (2018): 659–65. http://dx.doi.org/10.1007/s10958-018-3953-3.

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38

Varopoulos, N. Th. "Analysis on Lie groups." Journal of Functional Analysis 76, no. 2 (1988): 346–410. http://dx.doi.org/10.1016/0022-1236(88)90041-9.

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39

Trzetrzelewski, Maciej. "Supersymmetry and Lie groups." Journal of Mathematical Physics 48, no. 8 (2007): 083508. http://dx.doi.org/10.1063/1.2771418.

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40

Gadea, P. M., J. C. González-Dávila, and J. A. Oubiña. "Cyclic metric Lie groups." Monatshefte für Mathematik 176, no. 2 (2014): 219–39. http://dx.doi.org/10.1007/s00605-014-0692-5.

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41

Conti, Diego, and Federico A. Rossi. "Einstein nilpotent Lie groups." Journal of Pure and Applied Algebra 223, no. 3 (2019): 976–97. http://dx.doi.org/10.1016/j.jpaa.2018.05.010.

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42

Varopoulos, N. TH. "Diffusion on Lie Groups." Canadian Journal of Mathematics 46, no. 2 (1994): 438–48. http://dx.doi.org/10.4153/cjm-1994-023-5.

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43

Liu, Yanjun, and Wolfgang Willems. "Lie-type-like groups." Journal of Algebra 447 (February 2016): 432–44. http://dx.doi.org/10.1016/j.jalgebra.2015.08.023.

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44

Maier, Stephan. "Conformally flat Lie groups." Mathematische Zeitschrift 228, no. 1 (1998): 155–75. http://dx.doi.org/10.1007/pl00004600.

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45

Neeb, Karl-Hermann. "Weakly Exponential Lie Groups." Journal of Algebra 179, no. 2 (1996): 331–61. http://dx.doi.org/10.1006/jabr.1996.0015.

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46

Glöckner, Helge. "Lie Groups of Measurable Mappings." Canadian Journal of Mathematics 55, no. 5 (2003): 969–99. http://dx.doi.org/10.4153/cjm-2003-039-9.

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AbstractWe describe new construction principles for infinite-dimensional Lie groups. In particular, given any measure space (X; Σ, μ) and (possibly infinite-dimensional) Lie group G, we construct a Lie group L∞(X; G), which is a Fréchet-Lie group if G is so. We also show that the weak direct product of an arbitrary family (Gi)i∈I of Lie groups can be made a Lie group, modelled on the locally convex direct sum .

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47

Dobrev, V. K. "Invariant Differential Operators for Non-Compact Lie Groups: Euclidean Jordan Groups or Conformal Lie Groups." Journal of Physics: Conference Series 411 (January 28, 2013): 012012. http://dx.doi.org/10.1088/1742-6596/411/1/012012.

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48

Campagnolo, Caterina, and Holger Kammeyer. "Products of free groups in Lie groups." Journal of Algebra 579 (August 2021): 237–55. http://dx.doi.org/10.1016/j.jalgebra.2021.03.023.

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49

Kachi, Hideyuki, and Mamoru Mimura. "Homotopy groups of compact exceptional Lie groups." Proceedings of the Japan Academy, Series A, Mathematical Sciences 75, no. 4 (1999): 47–49. http://dx.doi.org/10.3792/pjaa.75.47.

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50

Stachura, Piotr. "From double Lie groups to quantum groups." Fundamenta Mathematicae 188 (2005): 195–240. http://dx.doi.org/10.4064/fm188-0-10.

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