Search results for "Secondary: 16R10"

Some characterizations of algebras with involution with polynomial growth of their codimensions

2018

Let A be an associative algebra endowed with an involution ∗ of the first kind and let c ∗n (A) denote the sequence of ∗-codimensions of A. In this paper, we are interested in algebras with involution such that the ∗-codimension sequence is polynomially bounded. We shall prove that A is of this kind if and only if it satisfies the same identities of a finite direct sum of finite dimensional algebras with involution A i , each of which with Jacobson radical of codimension less than or equal to one in A i . We shall also relate the condition of having polynomial codimension growth with the sequence of cocharacters and with the sequence of colengths. Along the way, we shall show that the multi…