Graded polynomial identities and Specht property for the Lie algebra of upper triangular matrices of order 3

TL;DR

This paper determines the graded polynomial identities for the Lie algebra of 3x3 upper triangular matrices with an elementary grading and examines the Specht property for these varieties.

Contribution

It provides explicit descriptions of graded identities and analyzes the Specht property for this specific Lie algebra class.

Findings

Computed graded polynomial identities for the algebra

Analyzed the Specht property for the variety

Extended understanding of graded identities in Lie algebras

Abstract

We compute the graded polynomial identities for the variety of graded algebras generated by the Lie algebra of upper triangular matrices of order 3 over an arbitrary field and endowed with an elementary grading. We investigate the Specht property for the same family of varieties.