Group gradings on classical Lie superalgebras

Abstract

We classify, up to isomorphism, the group gradings on the non-exceptional classical simple Lie superalgebras, except for type $A(1,1)$, over an algebraically closed field of characteristic zero. To this end, we study graded-simple and graded-superinvolution-simple associative superalgebras satisfying the descending chain condition on graded left superideals, which allows us to classify Abelian group gradings on finite-dimensional simple and superinvolution-simple associative superalgebras over an algebraically closed field of characteristic different from 2.