The polynomial part of the codimension growth of affine PI algebras

Let F be a field of characteristic zero and W an associative affine F -algebra satisfying a polynomial identity (PI). The codimension sequence cn(W)associated to W is known to be of the form Θ(n^t d^n), where d is the well known PI-exponent of W. In this paper we establish an algebraic interpretation of the polynomial part (the constant t) by means of Kemer's theory. In particular, we show that in case W is a basic algebra (hence finite dimensional), View the t = (q+d)/2 +s, where q is the number of simple component in W/J(W) and s+1 is the nilpotency degree of J(W) (the Jacobson radical of W). Thus proving a conjecture of Giambruno.

Trefwoorden:Codimension sequence, Kemer polynomials, Polynomial identity

Toegankelijkheid:Open