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Finite order automorphisms on real simple Lie algebras


Author: Meng-Kiat Chuah
Journal: Trans. Amer. Math. Soc. 364 (2012), 3715-3749
MSC (2010): Primary 17B20, 17B22, 17B40, 20B25
DOI: https://doi.org/10.1090/S0002-9947-2012-05604-2
Published electronically: February 15, 2012
MathSciNet review: 2901232
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Abstract | References | Similar Articles | Additional Information

Abstract: We add extra data to the affine Dynkin diagrams to classify all the finite order automorphisms on real simple Lie algebras. As applications, we study the extensions of automorphisms on the maximal compact subalgebras and also study the fixed point sets of automorphisms.


References [Enhancements On Off] (What's this?)

  • 1. M. K. Chuah and C. C. Hu, Equivalence classes of Vogan diagrams, J. Algebra 279 (2004), 22-37. MR 2078384 (2005g:17021)
  • 2. M. K. Chuah and J. S. Huang, Double Vogan diagrams and semisimple symmetric spaces, Trans. Amer. Math. Soc. 362 (2010), 1721-1750. MR 2574875 (2011a:17016)
  • 3. F. R. Gantmacher, Canonical representation of automorphisms of a complex semi-simple Lie group, Rec. Math. (Moscou) 5(47) (1939), 101-146. MR 0000998 (1:163d)
  • 4. S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Graduate Studies in Math. vol. 34, Amer. Math. Soc., Providence 2001. MR 1834454 (2002b:53081)
  • 5. J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer-Verlag, New York 1972. MR 0323842 (48:2197)
  • 6. V. G. Kac, Automorphisms of finite order of semisimple Lie algebras, Funkcional Anal. i Prilozen 3 (1969), 94-96. MR 0251091 (40:4322)
  • 7. V. G. Kac, Infinite Dimensional Lie Algebras, 3rd. ed., Cambridge Univ. Press, Cambridge 1990. MR 1104219 (92k:17038)
  • 8. A. W. Knapp, Lie Groups beyond an Introduction, 2nd. ed., Progr. Math. vol. 140, Birkhäuser, Boston 2002. MR 1920389 (2003c:22001)
  • 9. F. Levstein, A classification of involutive automorphisms of an affine Kac-Moody Lie algebra, J. Algebra 114 (1988), 489-518. MR 936987 (90g:17025)
  • 10. G. D. Mostow, Self-adjoint groups, Annals of Math. 62 (1955), 44-55. MR 0069830 (16:1088a)
  • 11. A. L. Onishchik and E. B. Vinberg, Lie Groups and Algebraic Groups, Springer-Verlag, Berlin, Heidelberg 1990. MR 1064110 (91g:22001)
  • 12. T. A. Springer, Linear Algebraic Groups, 2nd. ed., Progr. Math. vol. 9, Birkhäuser, Boston 1998. MR 1642713 (99h:20075)

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Additional Information

Meng-Kiat Chuah
Affiliation: Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan
Email: chuah@math.nthu.edu.tw

DOI: https://doi.org/10.1090/S0002-9947-2012-05604-2
Keywords: Real simple Lie algebra, Dynkin diagram, finite order automorphism
Received by editor(s): October 4, 2010
Received by editor(s) in revised form: January 4, 2011
Published electronically: February 15, 2012
Additional Notes: This work was supported in part by the National Science Council of Taiwan
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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