Graded deformations of skew group algebras for cyclic transvection groups acting on polynomial rings in positive characteristic
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912110816002048 |
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| author | Grimley, Lauren Krawzik, Naomi Lawson, Colin M. Uhl, Christine |
| author_facet | Grimley, Lauren Krawzik, Naomi Lawson, Colin M. Uhl, Christine |
| contents | We investigate deformations of skew group algebras that arise from a finite cyclic group acting on a polynomial ring in positive characteristic, where characteristic divides the order of the group. We allow deformations which deform both the group action and the vector space multiplication. We fully characterize the Poincare-Birkhoff-Witt deformations which arise in this setting from multiple perspectives: a necessary and sufficient condition list, a practical road map from which one can generate examples corresponding to any choice of group algebra element, an explicit formula, and a combinatorial analysis of the class of algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05181 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graded deformations of skew group algebras for cyclic transvection groups acting on polynomial rings in positive characteristic Grimley, Lauren Krawzik, Naomi Lawson, Colin M. Uhl, Christine Rings and Algebras 2020: 16E40, 16S35, 16E05, 16E30, 20C20, 20C08 We investigate deformations of skew group algebras that arise from a finite cyclic group acting on a polynomial ring in positive characteristic, where characteristic divides the order of the group. We allow deformations which deform both the group action and the vector space multiplication. We fully characterize the Poincare-Birkhoff-Witt deformations which arise in this setting from multiple perspectives: a necessary and sufficient condition list, a practical road map from which one can generate examples corresponding to any choice of group algebra element, an explicit formula, and a combinatorial analysis of the class of algebras. |
| title | Graded deformations of skew group algebras for cyclic transvection groups acting on polynomial rings in positive characteristic |
| topic | Rings and Algebras 2020: 16E40, 16S35, 16E05, 16E30, 20C20, 20C08 |
| url | https://arxiv.org/abs/2411.05181 |