ACTIONS OF LIE SUPERALGEBRAS ON SEMIPRIME ALGEBRAS WITH CENTRAL INVARIANTS

Abstract

AbstractLet R be a semiprime algebra over a field of characteristic zero acted finitely on by a finite-dimensional Lie superalgebra L = L0 ⊕ L1. It is shown that if L is nilpotent, [L0, L1] = 0 and the subalgebra of invariants RL is central, then the action of L0 on R is trivial and R satisfies the standard polynomial identity of degree 2 ⋅ [$\sqrt{2^{\dim_{\mathbb{K}}L_1}}$]. Examples of actions of nilpotent Lie superalgebras, with central invariants and with [L0, L1] ≠ 0, are constructed.