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 language||English (US)|
|Title of host publication||Group Theory, Algebra, and Number Theory|
|Subtitle of host publication||Colloquium in Memory of Hans Zassenhaus held in Saarbrücken, Germany, June 4-5, 1993|
|Publisher||De Gruyter Mouton|
|Number of pages||12|
|State||Published - Jul 20 2011|
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