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Twisted algebras of geometric algebras

Part of: Rings and algebras arising under various constructions Rings and algebras with additional structure Algebraic geometry: Foundations

Published online by Cambridge University Press:  18 October 2022

Masaki Matsuno Open the ORCID record for Masaki Matsuno [Opens in a new window]
Masaki Matsuno*
Affiliation:
Graduate School of Science and Technology, Shizuoka University, Ohya 836, Shizuoka 422-8529, Japan
*
e-mail: matsuno.masaki.14@shizuoka.ac.jp
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Abstract

A twisting system is one of the major tools to study graded algebras; however, it is often difficult to construct a (nonalgebraic) twisting system if a graded algebra is given by generators and relations. In this paper, we show that a twisted algebra of a geometric algebra is determined by a certain automorphism of its point variety. As an application, we classify twisted algebras of three-dimensional geometric Artin–Schelter regular algebras up to graded algebra isomorphism.

Keywords

Twisting systemstwisted algebrasgeometric algebrasAS-regular algebras

MSC classification

Primary: 14A22: Noncommutative algebraic geometry 16S38: Rings arising from non-commutative algebraic geometry
Secondary: 16W50: Graded rings and modules
Type
Article
Information
Canadian Mathematical Bulletin , Volume 66 , Issue 3 , September 2023 , pp. 715 - 730
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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Footnotes

The author was supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists (Grant No. 21J11303).

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