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arXiv · 1504.06299

Cocycle twists of algebras

Andrew Davies
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Abstract

Let $A = \bigoplus_{n=0}^{\infty}A_n$ be a connected graded $k$-algebra over an algebraically closed field $k$ (thus $A_0=k$). 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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Andrew Davies. 2015-04-23. Cocycle twists of algebras. https://arxiv.org/abs/1504.06299

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