A Lie algebra over a finite field of characteristic 2: Graded polynomial identities and Specht property

Abstract

Let K be a finite field of characteristic 2, and UT2:=UT2(K) be the Lie algebra of 2×2 upper triangular matrices over K with the multiplication x∘y=xy+yx=xy−yx. In this paper, we exhibit a finite basis of graded identities for the variety of Lie algebras generated by UT2 for any grading and show that it has the Specht property. It is important to highlight that the technique used in order to solve the Specht problem is independent of the characteristic of the field and also of its cardinality.