Simple Decompositions of Simple Lie Superalgebras

摘要

In this chapter we completely describe all isomorphism types of decompositions of the simple Lie superalgebra sl(rn.n) as the sum of two basic simple subalgebras. In this chapter we consider simple Lie superalgebras decomposable as the sum of two proper simple subalgebras. Any of these superalgebras have 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 structure of these sums has attracted considerable1 attention, mostly in the cases where A, B are (semi)simple or A,B are nilpotent.