Modelos Computacionais para Verificação de Identidades Polinomiais em Álgebras de Matrizes com entradas na Álgebra de Grassmann

ABSTRACT In this paper is presented a computational approach to deal with algebras that satisfy polynomial identities. More precisely, we used the Maple program to verify and identify polynomial identities of matrix algebras with entries in the Grassmann algebra E, especially the algebra M k,l (E), which Di Vincenzo and La Scala showed interesting results when k = l = 1, using the notion of weak polynomial identities. Some procedures were created in Maple to suit the product of the matrices according to the properties of E, this being a non-commutative algebra. In addition, we implemented some functions with shorter processing time in solving certain problems compared to similar Maple functions. It should be noted that we use the Maple version 18 on a computer with Intel @ Core i7 and 8GB of RAM memory. We conclude with a study of the conjecture given by Kemer at about the minimum degree of the standard polynomial for the algebra M n (E).