Graduações e identidades polinomiais graduadas para a álgebra de matrizes triangulares superiores

Abstract

Let F be a field and let G be a group. Denote by UTn(F) the algebra of n × n upper triangular matrices over F. The mathematicians Valenti and Zaicev described all G-gradings on UTn(F), and the mathematicians Di Vincenzo, Koshlukov and Valenti described the set of all G-graded polynomial identities of UTn(F) when F is an infinite field. After, Koshlukov and Yukihide described the elementary G-gradings on the Lie algebra UTn(F)^(−). In this dissertation, we study these results. Moreover, Koshlukov and Yukihide described the Zn-graded polynomial identities of the Lie algebra UTn(F)^(−) when the grading is canonical and F has characteristic 0. In this dissertation, we give another proof of this fact.