Identidades para álgebras de Lie especiais lineares com graduações de Pauli e Cartan.

Abstract

Let K be a field of characterist 0. In this work we describe a basis for the graded identities of the Lie algebra slp(K) with the Pauli grading, where p is prime number. Moreover, we compute their graded codimensions and show that the variety varZp×Zp(slp(K)) is minimal and satisfies the Specht property. We also describe a basis for the graded identities for the Lie algebra slm(K) with the Cartan grading by the group ℤm−1 and exibit a basis of the corresponding relatively free graded Lie algebra as vector space. As a corollary, we compute the graded codimensions for m=2 and provide a basis for the graded identities of certain Lie subalgebras of Mm(K)(−) with the Cartan grading.