Can one compute the exponential rate of growth of the ∗-codimensions of a PI-algebra with involution ∗ over a field of characteristic zero? It was shown ithat any such algebra A has the same ∗-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution B. Here, by exploiting this result we are able to provide an exact estimate of the exponential rate of growth exp∗(A) of any PI-algebra A with involution. It turns out that exp∗(A) is an integer and, in case the base field is algebraically closed, it coincides with the dimension of an admissible subalgebra of maximal dimension of B.
|Numero di pagine||21|
|Rivista||Journal of Algebra|
|Stato di pubblicazione||Published - 2017|
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory