Banca de DEFESA: PEDRO HENRIQUE MARTINS DE MORAIS

Gradings, graded polynominal identities and Specht Property for the Lie algebra of triangular superior matrices of order 2x2 in characteristic 2

Graded polynomial identities, Specht property, gradings.

In this paper, we present some recent results in PI-theory about gradings and graded polynomial
identities for the algebra of triangular superior matrices of order 2 when it is defined as a Lie algebra.
More precisely, fixed a field K of characteristic 2 (finite or infinite), we present a classification of the
gradings on (UT2(K ),◦), the algebra of triangular superior matrices of order 2 over K endowed with
the product defined by x ◦ y = x y + yx. We also show generators for the TG-ideals of these gradings
as well give a positive answer to the Specht problem for the variety of Lie algebras generated by
UT2(K ) for each of these gradings.