TY - JOUR

T1 - Group graded PI-algebras and their codimension growth

AU - Aljadeff, Eli

N1 - Funding Information:
∗The author was partially supported by the Israel Science Foundation (grant no. 1283/08) and by the E. Schaver Research Fund. Received February 9, 2010

PY - 2012/6

Y1 - 2012/6

N2 - Let W be an associative PI - algebra over a field F of characteristic zero. Suppose W is G-graded where G is a finite group. Let exp(W) and exp(We) denote the codimension growth of W and of the identity component We, respectively. The following inequality had been conjectured by Bahturin and Zaicev: exp(W) ≤ {pipe}G{pipe}2 exp(We). The inequality is known in case the algebra W is affine (i. e., finitely generated). Here we prove the conjecture in general.

AB - Let W be an associative PI - algebra over a field F of characteristic zero. Suppose W is G-graded where G is a finite group. Let exp(W) and exp(We) denote the codimension growth of W and of the identity component We, respectively. The following inequality had been conjectured by Bahturin and Zaicev: exp(W) ≤ {pipe}G{pipe}2 exp(We). The inequality is known in case the algebra W is affine (i. e., finitely generated). Here we prove the conjecture in general.

UR - http://www.scopus.com/inward/record.url?scp=84862591987&partnerID=8YFLogxK

U2 - 10.1007/s11856-011-0156-8

DO - 10.1007/s11856-011-0156-8

M3 - 文章

AN - SCOPUS:84862591987

SN - 0021-2172

VL - 189

SP - 189

EP - 205

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 1

ER -