Graded twisted Calabi-Yau algebras are generalized Artin-Schelter regular
| Autor: | Reyes, Manuel L., Rogalski, Daniel |
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| Rok vydání: | 2018 |
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| Zdroj: | Nagoya Mathematical Journal 245 (2022), 100-153 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/nmj.2020.32 |
| Popis: | 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. Comment: 54 pages. Title has been changed (formerly titled "A twisted Calabi-Yau toolkit"). Revisions to the writing throughout |
| Databáze: | arXiv |
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