Graded polynomial identities and exponential growth

TY - JOUR

T1 - Graded polynomial identities and exponential growth

AU - Aljadeff, Eli

AU - Giambruno, Antonio

AU - La Mattina, Daniela

PY - 2011/1

Y1 - 2011/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79551639739&partnerID=8YFLogxK

U2 - 10.1515/CRELLE.2011.004

DO - 10.1515/CRELLE.2011.004

M3 - 文章

AN - SCOPUS:79551639739

SN - 0075-4102

SP - 83

EP - 100

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

IS - 650

ER -