The Calabi–Yau property of Ore extensions of two-dimensional Artin–Schelter regular algebras and their PBW deformations

Yuan Shen; Yang Guo

doi:10.5802/crmath.268

Algèbre

The Calabi–Yau property of Ore extensions of two-dimensional Artin–Schelter regular algebras and their PBW deformations

Yuan Shen ¹ ; Yang Guo ¹

¹ Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, China

Comptes Rendus. Mathématique, Volume 360 (2022), pp. 739-749.

Résumé

Let $A$ be a noncommutative Artin–Schelter regular algebra of dimension $2$ with the Nakayama automorphism $μ_{A}$ and $U$ a PBW deformation of $A$ with the Nakayama automorphism $μ_{U}$ . We prove that any graded Ore extension $A [z; μ_{A}, δ]$ and any filtered Ore extension $U [z; μ_{U}, \tilde{δ}]$ are $3$ -Calabi–Yau.

Reçu le : 2021-08-10
Révisé le : 2021-09-05
Accepté le : 2021-09-06
Publié le : 2022-06-30

DOI : 10.5802/crmath.268

Classification : 16S36, 16S37, 16S38, 16S80, 16E65

Affiliations des auteurs :

Yuan Shen ¹ ; Yang Guo ¹

¹ Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, China

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

@article{CRMATH_2022__360_G7_739_0,
     author = {Yuan Shen and Yang Guo},
     title = {The {Calabi{\textendash}Yau} property of {Ore} extensions of two-dimensional {Artin{\textendash}Schelter} regular algebras and their {PBW} deformations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {739--749},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     year = {2022},
     doi = {10.5802/crmath.268},
     language = {en},
}

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Yuan Shen; Yang Guo. The Calabi–Yau property of Ore extensions of two-dimensional Artin–Schelter regular algebras and their PBW deformations. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 739-749. doi : 10.5802/crmath.268. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.268/

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