Specht property of varieties of graded Lie algebras

Autor(es)

Correa, Daniela Martinez ; Koshlukov, Plamen

• Tipo de documento: Artigo Científico
• Fonte: MONATSHEFTE FUR MATHEMATIK; v. N/A, p. 28-pg., 2023-03-27.

Resumo

Let UTn(F) be the algebra of the nxn upper triangular matrices and denote UTn(F)((-)) the Lie algebra on the vector space of UTn(F) with respect to the usual bracket (commutator), over an infinite field F. In this paper, we give a positive answer to the Specht property for the ideal of the Z(n)-graded identities of UTn(F)((-)) with the canonical grading when the characteristic p of F is 0 or is larger than n-1. Namely we prove that every ideal of graded identities in the free graded Lie algebra that contains the graded identities of UTn(F)((-)), is finitely based. Moreover we show that if F is an infinite field of characteristic p = 2 then the Z(3)-graded identities of UT(-) (3) (F) do not satisfy the Specht property. More precisely, we construct explicitly an ideal of graded identities containing that of UT(-) (3) (F), and which is not finitely generated as an ideal of graded identities. (AU)

• Processo FAPESP: 18/23690-6 - Estruturas, representações e aplicações de sistemas algébricos
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Temático