Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Cartan algebras and involutions


Author: Karlheinz Spindler
Journal: Proc. Amer. Math. Soc. 121 (1994), 323-333
MSC: Primary 17B05
DOI: https://doi.org/10.1090/S0002-9939-1994-1169049-5
MathSciNet review: 1169049
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We identify Cartan algebras in certain semidirect products and prove that every involution of a real Lie algebra leaves invariant some Cartan algebra. Moreover, we establish the adaptability of invariant Cartan algebras and invariant Levi decompositions and prove some conjugacy theorems for invariant Cartan algebras.


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

  • [1] N. Bourbaki, Éléments de mathématique. Fasc. XXXVIII: Groupes et algèbres de Lie. Chapitre VII: Sous-algèbres de Cartan, éléments réguliers. Chapitre VIII: Algèbres de Lie semi-simples déployées, Actualités Scientifiques et Industrielles, No. 1364. Hermann, Paris, 1975 (French). MR 0453824
  • [2] Sigurdur Helgason, Differential geometry, Lie groups, and symmetric spaces, Pure and Applied Mathematics, vol. 80, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 514561
  • [3] Joachim Hilgert, Karl Heinrich Hofmann, and Jimmie D. Lawson, Lie groups, convex cones, and semigroups, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1989. Oxford Science Publications. MR 1032761
  • [4] Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol I, Interscience Publishers, a division of John Wiley & Sons, New York-London, 1963. MR 0152974
  • [5] Henrik Schlichtkrull, Hyperfunctions and harmonic analysis on symmetric spaces, Progress in Mathematics, vol. 49, Birkhäuser Boston, Inc., Boston, MA, 1984. MR 757178
  • [6] Garth Warner, Harmonic analysis on semi-simple Lie groups. I, Springer-Verlag, New York-Heidelberg, 1972. Die Grundlehren der mathematischen Wissenschaften, Band 188. MR 0498999

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 17B05

Retrieve articles in all journals with MSC: 17B05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1169049-5
Article copyright: © Copyright 1994 American Mathematical Society