Involution Codimensions of Finite Dimensional Algebras and Exponential Growth

Let F be a field of characteristic zero and let A be a finite dimensional algebra with involution * over F. We study the asymptotic behavior of the sequence of * -codimensions cn(A, * ) of A and we show that exists and is an integer. We give an explicit way for computing Exp(A, * ) and as a consequence we obtain the following characterization of * -simple algebras: A is * -simple if and only if Exp(A, * ) = dimF A.