Untwisting a twisted Calabi–Yau algebra

Goodman, J. and Krahmer, U. (2014) Untwisting a twisted Calabi–Yau algebra. Journal of Algebra, 406, pp. 272-289. (doi: 10.1016/j.jalgebra.2014.02.018)

Abstract

Twisted Calabi–Yau algebras are a generalisation of Ginzburg's notion of Calabi–Yau algebras. Such algebras A come equipped with a modular automorphism  σ∈Aut(A), the case σ=id being precisely the original class of Calabi–Yau algebras. The aim of this paper is to give a concise proof of the fact that every twisted Calabi–Yau algebra may be extended to a Calabi–Yau algebra. More precisely, we show that if A is a twisted Calabi–Yau algebra with modular automorphism σ  , then the smash (semidirect) product algebras A⋊σN and A⋊σZ are Calabi–Yau.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Goodman, Mr Jake and Kraehmer, Dr Ulrich
• Authors: Goodman, J., and Krahmer, U.
• College/School: College of Science and Engineering > School of Mathematics and Statistics
• Journal Name: Journal of Algebra
• Publisher: Elsevier Inc.
• ISSN: 0021-8693
• ISSN (Online): 1090-266X