Graded PI-exponents of simple Lie superalgebras

TL;DR

This paper investigates the graded polynomial identities of simple Lie superalgebras over characteristic zero fields and establishes the existence of their graded PI-exponent, advancing understanding of their algebraic structure.

Contribution

It proves the existence of the graded PI-exponent for simple Lie superalgebras, a key step in understanding their polynomial identity growth.

Findings

Existence of graded PI-exponent established

Provides new insights into the structure of Lie superalgebras

Advances the theory of polynomial identities in superalgebras

Abstract

We study $\mathbb{Z}_2$-graded identities of simple Lie superalgebras over a field of characteristic zero. We prove the existence of the graded PI-exponent for such algebras.