On the codimension growth of simple color Lie superalgebras

TL;DR

This paper investigates the exponential growth of polynomial identities in finite dimensional simple color Lie superalgebras, establishing that the growth rate equals the algebra's dimension, with similar results for graded identities.

Contribution

It proves that the codimension growth rate of identities in simple color Lie superalgebras equals their dimension, extending known results to graded identities.

Findings

Codimensions grow exponentially with rate equal to the algebra's dimension

Results apply to both identities and graded identities

Establishes a link between algebra structure and polynomial identity growth

Abstract

We study polynomial identities of finite dimensional simple color Lie superalgebras over an algebraically closed field of characteristic zero graded by the product of two cyclic groups of order $2$. We prove that the codimensions of identities grow exponentially and the rate of exponent equals the dimension of the algebra. A similar result is also obtained for graded identities and graded codimensions.