Group gradings on classical Lie superalgebras

TL;DR

This paper classifies group gradings on classical simple Lie superalgebras over algebraically closed fields of characteristic zero, extending understanding of their algebraic structures and symmetries.

Contribution

It provides a comprehensive classification of group gradings on non-exceptional classical Lie superalgebras, excluding type A(1,1), using associative superalgebra techniques.

Findings

Classified gradings on classical Lie superalgebras.

Developed methods for associative superalgebra gradings.

Extended classification to superinvolution-simple cases.

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.