Let G be a finite group and A a finite dimensional G-graded algebra over a
field of characteristic zero. When A is simple as a G-graded algebra, by mean
of Regev central polynomials we construct multialternating graded polynomials
of arbitrarily large degree non vanishing on A. As a consequence we compute the
exponential rate of growth of the sequence of graded codimensions of an
arbitrary G-graded algebra satisfying an ordinary polynomial identity. In
particular we show it is an integer.
The result was proviously known in case G is abelian.Comment: To appear in Proc. of AM
