Simple decompositions of simple Lie superalgebras

2005/09/03 by T. Tvalavadze, Tvalavadze, T.
Mathematics · #17B20 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:17B20

paper · pdf · doi:10.48550/arxiv.math/0509065

arxiv created 2005/09/03 · arxiv updated 2009/12/01

Abstract

In this paper we consider Lie superalgebras decomposable as the sum of two proper subalgebras. Any of these algebras has the form of the vector space sum L=A+B where A and B are proper simple subalgebras which need not be ideals of L, and the sum need not be direct. The main result of this paper is the following: Let S = osp(m,2n) be a Lie superalgebra such that S=K+L where K, L are two proper basic simple subalgebras. Then m is even, m=2k and K ≅ osp(2k-1,2n), L ≅ sl(k,n).

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