Cartan subspaces of symmetric lie algebras

J. Lepowsky, G. W. McCollum

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

A symmetric Lie algebra is defined, following J. Dixmier, to be a Lie algebra 9 with a decomposition g = t ⨁ p such that l is a subalgebra of g,[t, p]⊂p and [p, p] ⊂t. A definition of Cartan subspace of a symmetric Lie algebra is given, and a theory is presented which parallels the standard theory of Cartan subalgebras of Lie algebras, and which generalizes the classical results for real and complex semisimple symmetric Lie algebras.

Original languageEnglish (US)
Pages (from-to)217-228
Number of pages12
JournalTransactions of the American Mathematical Society
Volume216
DOIs
StatePublished - 1976
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Cartan subspaces
  • Natural b -subalgebras
  • Nil subspaces
  • Reductive symmetric Lie algebras
  • Splitting Cartan subspaces
  • Symmetric Lie algebras
  • Weight theory for nil sets

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