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In this paper, we study the growth of the codimensions of a finite dimensional-superalgebraover a field of characteristic zero. We prove thathas polynomial growth if and only if any finite dimensional-superalgebra satisfying the same-graded identities ofhas an explicit decomposition into suitable-superalgebras. We also give such a characterization by studying the decomposition of the-cocharacter of. In this case, the main tool is the representation theory of the product of symmetric groups. [ABSTRACT FROM PUBLISHER]

We study the growth of the codimensions of a *-superalgebra over a field of characteristic zero. We classify the ideals of identities of finite dimensional algebras whose corresponding codimensions are of almost polynomial growth. It turns out that these are the ideals of identities of two algebras with distinct involutions and gradings. Along the way, we also classify the finite dimensional simple *-superalgebras over an algebraically closed field of characteristic zero. [ABSTRACT FROM PUBLISHER]