On the solvability of the kernel of any orthogonal decomposition

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The aim of the article is to make a step toward the classification of orthogonal decompositions of complex simple Lie algebras. Namely, we show that the kernel of an orthogonal decomposition of a complex simple Lie algebra L(i.e., the group consisting of all automorphisms of Lthat act trivially on the set of components of the decomposition) is near to be soluble. An essential ingredient of our arguments is a long-standing theorem of H. Zassenhaus characterizing the group SL 2 (5).

Original languageEnglish (US)
Title of host publicationGroup Theory, Algebra, and Number Theory
Subtitle of host publicationColloquium in Memory of Hans Zassenhaus held in Saarbrücken, Germany, June 4-5, 1993
PublisherDe Gruyter Mouton
Pages1-12
Number of pages12
ISBN (Electronic)9783110811957
ISBN (Print)9783110153477
StatePublished - Jul 20 2011
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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  • Cite this

    Tiep, P. H. (2011). On the solvability of the kernel of any orthogonal decomposition. In Group Theory, Algebra, and Number Theory: Colloquium in Memory of Hans Zassenhaus held in Saarbrücken, Germany, June 4-5, 1993 (pp. 1-12). De Gruyter Mouton.