On group gradings on PI-algebras

Eli Aljadeff; Ofir David

doi:10.1016/j.jalgebra.2014.12.042

On group gradings on PI-algebras

Eli Aljadeff, Ofir David^*

^*Corresponding author for this work

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

4 Scopus citations

Abstract

We show that there exists a constant K such that for any PI-algebra W and any nondegenerate G-grading on W where G is any group (possibly infinite), there exists an abelian subgroup U of G with [G:U]≤exp(W)^K. A G-grading W=⊕_g∈GW_g is said to be nondegenerate if W_g1W_g2.W_gr≠0 for any r≥1 and any r tuple (g₁, g₂,., g_r) in G^r.

Original language	English
Pages (from-to)	403-424
Number of pages	22
Journal	Journal of Algebra
Volume	428
DOIs	https://doi.org/10.1016/j.jalgebra.2014.12.042
State	Published - 5 Apr 2015
Externally published	Yes

Keywords

Codimension growth
Graded algebra
Polynomial identity

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title = "On group gradings on PI-algebras",

abstract = "We show that there exists a constant K such that for any PI-algebra W and any nondegenerate G-grading on W where G is any group (possibly infinite), there exists an abelian subgroup U of G with [G:U]≤exp(W)K. A G-grading W=⊕g∈GWg is said to be nondegenerate if Wg1Wg2.Wgr≠0 for any r≥1 and any r tuple (g1, g2,., gr) in Gr.",

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author = "Eli Aljadeff and Ofir David",

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AU - David, Ofir

PY - 2015/4/5

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N2 - We show that there exists a constant K such that for any PI-algebra W and any nondegenerate G-grading on W where G is any group (possibly infinite), there exists an abelian subgroup U of G with [G:U]≤exp(W)K. A G-grading W=⊕g∈GWg is said to be nondegenerate if Wg1Wg2.Wgr≠0 for any r≥1 and any r tuple (g1, g2,., gr) in Gr.

AB - We show that there exists a constant K such that for any PI-algebra W and any nondegenerate G-grading on W where G is any group (possibly infinite), there exists an abelian subgroup U of G with [G:U]≤exp(W)K. A G-grading W=⊕g∈GWg is said to be nondegenerate if Wg1Wg2.Wgr≠0 for any r≥1 and any r tuple (g1, g2,., gr) in Gr.

KW - Codimension growth

KW - Graded algebra

KW - Polynomial identity

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U2 - 10.1016/j.jalgebra.2014.12.042

DO - 10.1016/j.jalgebra.2014.12.042

M3 - 文章

AN - SCOPUS:84922422568

SN - 0021-8693

VL - 428

SP - 403

EP - 424

JO - Journal of Algebra

JF - Journal of Algebra

ER -

On group gradings on PI-algebras

Abstract

Keywords

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