Identities for the Lie algebra gl(2) over an infinite field of characteristic two

TL;DR

This paper investigates the polynomial identities of the Lie algebra gl(2) over an infinite field of characteristic two, providing a generating set for the ideal of identities where none was previously known.

Contribution

It establishes a generating set for the T-ideal of polynomial identities of gl(2) in characteristic two, advancing understanding of its algebraic structure.

Findings

Identified a generating set for the T-ideal T[gl(2)]

Extended previous results on polynomial identities in characteristic two

Clarified the structure of identities for gl(2) in this setting

Abstract

In 1970 Vaughan-Lee established that over an infinite field of characteristic two the ideal T[gl(2)] of all polynomial identities for the Lie algebra gl(2) is not finitely generated as a T-ideal. But a generating set for this ideal of polynomial identities was not found. We establish some generating set for the T-ideal T[gl(2)].