# Pauli gradings on Lie superalgebras and graded codimension growth

## TL;DR

This paper introduces a new grading on finite-dimensional simple Lie superalgebras using elementary abelian 2-groups, leading to the computation of graded PI-exponents and advancing understanding of polynomial identities in these structures.

## Contribution

It generalizes existing gradings on Lie superalgebras and computes the graded PI-exponent for the introduced Pauli grading.

## Key findings

- Computed the graded PI-exponent for Pauli grading.
- Established a new grading framework using elementary abelian 2-groups.
- Extended the understanding of polynomial identities in Lie superalgebras.

## Abstract

We introduce grading on certain finite dimensional simple Lie superalgebras of type $P(t)$ by elementary abelian 2-group. This grading gives rise to Pauli matrices and is a far generalization of $(\mathbb Z_2\times \mathbb Z_2)$-grading on Lie algebra of $(2\times 2)$-traceless matrices.We use this grading for studying numerical invariants of polyomial identities of Lie superalgebras. In particular, we compute graded PI-exponent corresponding to Pauli grading.