On deformations of crossed products

Eli Aljadeff; Yuval Ginosar; Andy R. Magid

doi:10.1016/j.jpaa.2006.08.015

On deformations of crossed products

Eli Aljadeff^*, Yuval Ginosar, Andy R. Magid

^*Corresponding author for this work

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

Abstract

Let A * Γ be a crossed product algebra, where A is semisimple, finitely generated over its center and Γ is a finite group. We give a necessary and sufficient condition in terms of the outer action of Γ on A for the existence of a multi-parametric semisimple deformation of the form A ((t₁, ..., t_n)) * Γ (with the induced outer action). The main tool in the proof is the solution of the so-called twisting problem. We also give an example which shows that the condition is not sufficient if one drops the condition on the finite generation of A over its center.

Original language	English
Pages (from-to)	81-91
Number of pages	11
Journal	Journal of Pure and Applied Algebra
Volume	210
Issue number	1
DOIs	https://doi.org/10.1016/j.jpaa.2006.08.015
State	Published - Jul 2007
Externally published	Yes

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abstract = "Let A * Γ be a crossed product algebra, where A is semisimple, finitely generated over its center and Γ is a finite group. We give a necessary and sufficient condition in terms of the outer action of Γ on A for the existence of a multi-parametric semisimple deformation of the form A ((t1, ..., tn)) * Γ (with the induced outer action). The main tool in the proof is the solution of the so-called twisting problem. We also give an example which shows that the condition is not sufficient if one drops the condition on the finite generation of A over its center.",

author = "Eli Aljadeff and Yuval Ginosar and Magid, {Andy R.}",

year = "2007",

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AU - Aljadeff, Eli

AU - Ginosar, Yuval

AU - Magid, Andy R.

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AB - Let A * Γ be a crossed product algebra, where A is semisimple, finitely generated over its center and Γ is a finite group. We give a necessary and sufficient condition in terms of the outer action of Γ on A for the existence of a multi-parametric semisimple deformation of the form A ((t1, ..., tn)) * Γ (with the induced outer action). The main tool in the proof is the solution of the so-called twisting problem. We also give an example which shows that the condition is not sufficient if one drops the condition on the finite generation of A over its center.

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On deformations of crossed products

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