Identidades polinomiais na algebra das matrizes de ordem 2

AUTOR(ES)

Jones Colombo

DATA DE PUBLICAÇÃO

2004

RESUMO

In chapter 1 we establish the results and notations that will be used in the rest of the text. For us K is an infinite field of characteristic different from 2. In chapter 2 we discuss the polynomials identities satisfied by the matrix algebra of order 2 over the field K. At the end of the chapter we find a minimal basis for the identities of this algebra in the cases where a characteristic of field K is 3 and 5. In chapter 3 we study the centrals polynomials in the matrix algebra of order 2 over field K. Following Okthitin’s ideas and applying the results of chapter 2, we describe a basis of the T-space of central polynomials. In chapter 4 we consider the identities with involution for matrix algebra of order 2 over field K. We describe the basis of the identities with involution for this algebra. We consider both of the types of involution, the transpose and the sympletic.

ASSUNTO(S)

polinomios algebra algebra não-comutativa

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