Cocycle twists of algebras

2015/04/23 by Andrew Davies, Davies, Andrew · 1 citation
Mathematics · #16S35 #16S38 (Primary) #16W22 (Secondary) #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16S35 #msc:16S38 #msc:16W22

paper · pdf · doi:10.48550/arxiv.1504.06299

17 pages

arxiv created 2015/04/23 · openalex publication_date 2015/04/23 · arxiv updated 2015/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A = \bigoplus_n=0^∞A_n be a connected graded k-algebra over an algebraically closed field k (thus A₀=k). Assume that a finite abelian group G, of order coprime to the characteristic of k, acts on A by graded automorphisms. In conjunction with a suitable cocycle this action can be used to twist the multiplication in A. We study this new structure and, in particular, we describe when properties like Artin-Schelter regularity are preserved by such a twist. We then apply these results to examples of Rogalski and Zhang.

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• Some components of the moduli space of Koszul Artin-Schelter regular algebras of dimension four

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