Identidades satisfeitas por álgebras com estruturas adicionais e multiplicidades limitadas por constante

Abstract

In this dissertation, we establish conditions for the multiplicities in the cocharacter decomposition of a given algebra to be bounded by a constant via identities satisfied by the algebra. Such conditions are established in the context of algebras with additional structures and we study such situations for algebras endowed with involution and for superalgebras with graded involution. Moreover, for an algebra graded by a finite group, we determine a necessary and sufficient condition for the multiplicities to be bounded by constant via particular identities that the algebra satisfies and for an algebra A graded by a finite group and endowed with a graded involution, we present a characterization for A to have multiplicities bounded by 1 from specific identities that are satisfied by it.