The Calabi–Yau property of Ore extensions of two-dimensional Artin–Schelter regular algebras and their PBW deformations
Let $A$ be a noncommutative Artin–Schelter regular algebra of dimension $2$ with the Nakayama automorphism $\mu _A$ and $U$ a PBW deformation of $A$ with the Nakayama automorphism $\mu _U$. We prove that any graded Ore extension $A[z;\mu _A,\delta ]$ and any filtered Ore extension $U[z;\mu _U,\tilde...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2022-06-01
|
| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.268/ |
| _version_ | 1797651466542907392 |
|---|---|
| author | Shen, Yuan Guo, Yang |
| author_facet | Shen, Yuan Guo, Yang |
| author_sort | Shen, Yuan |
| collection | DOAJ |
| description | Let $A$ be a noncommutative Artin–Schelter regular algebra of dimension $2$ with the Nakayama automorphism $\mu _A$ and $U$ a PBW deformation of $A$ with the Nakayama automorphism $\mu _U$. We prove that any graded Ore extension $A[z;\mu _A,\delta ]$ and any filtered Ore extension $U[z;\mu _U,\tilde{\delta }]$ are $3$-Calabi–Yau. |
| first_indexed | 2024-03-11T16:16:09Z |
| format | Article |
| id | doaj.art-50f6fc89b4e44c17a5419b531009ca2c |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:16:09Z |
| publishDate | 2022-06-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-50f6fc89b4e44c17a5419b531009ca2c2023-10-24T14:19:36ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692022-06-01360G773974910.5802/crmath.26810.5802/crmath.268The Calabi–Yau property of Ore extensions of two-dimensional Artin–Schelter regular algebras and their PBW deformationsShen, Yuan0Guo, Yang1Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, ChinaDepartment of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, ChinaLet $A$ be a noncommutative Artin–Schelter regular algebra of dimension $2$ with the Nakayama automorphism $\mu _A$ and $U$ a PBW deformation of $A$ with the Nakayama automorphism $\mu _U$. We prove that any graded Ore extension $A[z;\mu _A,\delta ]$ and any filtered Ore extension $U[z;\mu _U,\tilde{\delta }]$ are $3$-Calabi–Yau.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.268/ |
| spellingShingle | Shen, Yuan Guo, Yang The Calabi–Yau property of Ore extensions of two-dimensional Artin–Schelter regular algebras and their PBW deformations Comptes Rendus. Mathématique |
| title | The Calabi–Yau property of Ore extensions of two-dimensional Artin–Schelter regular algebras and their PBW deformations |
| title_full | The Calabi–Yau property of Ore extensions of two-dimensional Artin–Schelter regular algebras and their PBW deformations |
| title_fullStr | The Calabi–Yau property of Ore extensions of two-dimensional Artin–Schelter regular algebras and their PBW deformations |
| title_full_unstemmed | The Calabi–Yau property of Ore extensions of two-dimensional Artin–Schelter regular algebras and their PBW deformations |
| title_short | The Calabi–Yau property of Ore extensions of two-dimensional Artin–Schelter regular algebras and their PBW deformations |
| title_sort | calabi yau property of ore extensions of two dimensional artin schelter regular algebras and their pbw deformations |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.268/ |
| work_keys_str_mv | AT shenyuan thecalabiyaupropertyoforeextensionsoftwodimensionalartinschelterregularalgebrasandtheirpbwdeformations AT guoyang thecalabiyaupropertyoforeextensionsoftwodimensionalartinschelterregularalgebrasandtheirpbwdeformations AT shenyuan calabiyaupropertyoforeextensionsoftwodimensionalartinschelterregularalgebrasandtheirpbwdeformations AT guoyang calabiyaupropertyoforeextensionsoftwodimensionalartinschelterregularalgebrasandtheirpbwdeformations |