Group graded PI-algebras and their codimension growth

Eli Aljadeff

doi:https://doi.org/10.1007/s11856-011-0156-8

Group graded PI-algebras and their codimension growth

Eli Aljadeff

Mathematics

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

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(W_e) denote the codimension growth of W and of the identity component W_e, respectively. The following inequality had been conjectured by Bahturin and Zaicev: exp(W) ≤ {pipe}G{pipe}² exp(W_e). The inequality is known in case the algebra W is affine (i. e., finitely generated). Here we prove the conjecture in general.

Original language	English
Pages (from-to)	189-205
Number of pages	17
Journal	Israel Journal of Mathematics
Volume	189
Issue number	1
DOIs	https://doi.org/10.1007/s11856-011-0156-8
State	Published - Jun 2012

All Science Journal Classification (ASJC) codes

General Mathematics

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title = "Group graded PI-algebras and their codimension growth",

abstract = "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.",

author = "Eli Aljadeff",

note = "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",

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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.

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U2 - https://doi.org/10.1007/s11856-011-0156-8

DO - https://doi.org/10.1007/s11856-011-0156-8

M3 - مقالة

SN - 0021-2172

VL - 189

SP - 189

EP - 205

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 1

ER -

Group graded PI-algebras and their codimension growth

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