Search results for " 16P90"
showing 2 items of 2 documents
Multialternating graded polynomials and growth of polynomial identities
2012
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.
Graded polynomial identities and exponential growth
2009
Let $A$ be a finite dimensional algebra over a field of characteristic zero graded by a finite abelian group $G$. Here we study a growth function related to the graded polynomial identities satisfied by $A$ by computing the exponential rate of growth of the sequence of graded codimensions of $A$. We prove that the $G$-exponent of $A$ exists and is an integer related in an explicit way to the dimension of a suitable semisimple subalgebra of $A$.