Proceedings of the Indian Academy of Sciences - Mathematical Sciences

, 91:167

On invariant convex cones in simple Lie algebras

  • S. Kumaresan
  • Akhil Ranjan
Article

DOI: 10.1007/BF02881028

Cite this article as:
Kumaresan, S. & Ranjan, A. Proc. Indian Acad. Sci. (Math. Sci.) (1982) 91: 167. doi:10.1007/BF02881028

Abstract

This paper is devoted to a study and classification ofG-invariant convex cones ing, whereG is a lie group andg its Lie algebra which is simple. It is proved that any such cone is characterized by its intersection withh-a fixed compact Cartan subalgebra which exists by the very virtue of existence of properG-invariant cones. In fact the pair (g,k) is necessarily Hermitian symmetric.

Keywords

Lie algebraadjoint groupinvariant convex cones

Copyright information

© Indian Academy of Sciences 1982

Authors and Affiliations

  • S. Kumaresan
    • 1
  • Akhil Ranjan
    • 1
  1. 1.School of MathematicsTata Institute of Fundamental ResearchBombayIndia