Identidades polinomiais graduadas para a álgebra de matrizes triangulares superiores sobre um corpo finito.

Abstract

Let K be a finite field, G a group, and UTn the algebra of upper triangular matrices of order n x n over K. In this dissertation, we study the elementary gradings on UTn and their graded polynomial identities. We classify all the gradings on UTn, proving that every G—grading on UTn is isomorphic to an elementary grading. Furthermore, we prove that two elementary gradings coincide if and only if they satisfy the same graded identities. Finally, we obtain the main result of this work: an explicit description of a basis for the TG—ideal of graded polynomial identities of UTn, for any fixed elementary grading. If the group G is finite, then the obtained basis is finite.