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Simple decompositions of simple Lie superalgebras

T. Tvalavadze
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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 $K \cong osp(2k-1,2n)$, $L \cong sl(k,n)$.

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T. Tvalavadze. 2005-09-03. Simple decompositions of simple Lie superalgebras. https://arxiv.org/abs/math/0509065

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