Graded polynomial identities and exponential growth
Rings and Algebras
2009-03-12 v1
Abstract
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.
Cite
@article{arxiv.0903.1860,
title = {Graded polynomial identities and exponential growth},
author = {Eli Aljadeff and Antonio Giambruno and Daniela La Mattina},
journal= {arXiv preprint arXiv:0903.1860},
year = {2009}
}