Group gradings on the classical lie superalgebras Q(n), P(n) and B(m,n)

Abstract

Let G be an abelian group. We classify, up to isomorphism, the G-gradings on the classical Lie superalgebras B, P and Q, as well as the fine gradings up to equivalence. Also, we revisit the problem for the associative matrix superalgebras. Everything is done over an algebraically closed field of characteristic zero. In summary, this work completes the classification of the group gradings for some of the non-exceptional classical Lie superalgebras. Part of this work is published in [1] and [9].