Graded codimensions of Lie superalgebra $b(2)$

TL;DR

This paper investigates the asymptotic growth of graded codimensions in the Lie superalgebra b(2), establishing the existence and exact value of its graded PI-exponent.

Contribution

It proves the existence of the graded PI-exponent for b(2) and calculates its precise value, advancing understanding of Lie superalgebra identities.

Findings

Graded PI-exponent of b(2) exists and equals 3+2√3.

Asymptotic behavior of graded codimensions is characterized.

Provides new insights into the structure of Lie superalgebra identities.

Abstract

We study asymptotic behaviour of graded codimensions of Lie superalgebra $b(2)$. We prove that graded PI-exponent exists and is equal to $3+2\sqrt 3$.