Non-Matrix Polynomial identity enveloping algebras

TL;DR

This paper characterizes restricted Lie superalgebras whose enveloping algebras satisfy non-matrix polynomial identities, providing insights into their algebraic structure in characteristic p>2.

Contribution

It offers a characterization of restricted Lie superalgebras based on the polynomial identities satisfied by their enveloping algebras, focusing on non-matrix identities.

Findings

Characterization of L when u(L) satisfies a non-matrix polynomial identity

Identification of conditions under which u(L) satisfies such identities

Insights into the structure of restricted Lie superalgebras in characteristic p>2

Abstract

Let L be a restricted Lie superalgebra with its restricted enveloping algebra u(L) over a field F of characteristic p>2. A polynomial identity is called non-matrix if it is not satisfied by the algebra of 2\times 2 matrices over F. We characterize L when u(L) satisfies a non-matrix polynomial identity.