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- W3081477891 abstract "Abstract This is a general study of twisted Calabi–Yau algebras that are $mathbb {N}$ -graded and locally finite-dimensional, with the following major results. We prove that a locally finite graded algebra is twisted Calabi–Yau if and only if it is separable modulo its graded radical and satisfies one of several suitable generalizations of the Artin–Schelter regularity property, adapted from the work of Martinez-Villa as well as Minamoto and Mori. We characterize twisted Calabi–Yau algebras of dimension 0 as separable k -algebras, and we similarly characterize graded twisted Calabi–Yau algebras of dimension 1 as tensor algebras of certain invertible bimodules over separable algebras. Finally, we prove that a graded twisted Calabi–Yau algebra of dimension 2 is noetherian if and only if it has finite GK dimension." @default.
- W3081477891 created "2020-09-01" @default.
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- W3081477891 date "2021-02-02" @default.
- W3081477891 modified "2023-10-16" @default.
- W3081477891 title "GRADED TWISTED CALABI–YAU ALGEBRAS ARE GENERALIZED ARTIN–SCHELTER REGULAR" @default.
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- W3081477891 doi "https://doi.org/10.1017/nmj.2020.32" @default.
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