Some Artin-Schelter Regular Algebras From Dual Reflection Groups and their Geometry
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913542026821632 |
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| author | Goetz, Peter Kirkman, Ellen E. Moore, W. Frank Vashaw, Kent B. |
| author_facet | Goetz, Peter Kirkman, Ellen E. Moore, W. Frank Vashaw, Kent B. |
| contents | Let $G$ be a group coacting on an Artin-Schelter regular algebra $A$ homogeneously and inner-faithfully. When the identity component $A_e$ is also Artin-Schelter regular, providing a generalization of the Shephard-Todd-Chevalley Theorem, we say that $G$ is a dual reflection group for $A$. We give two examples of dual reflection groups of order 16, and study algebraic and geometric properties of three associated Artin-Schelter regular algebras of dimension four. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_08959 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some Artin-Schelter Regular Algebras From Dual Reflection Groups and their Geometry Goetz, Peter Kirkman, Ellen E. Moore, W. Frank Vashaw, Kent B. Rings and Algebras Quantum Algebra 16S38, 16W22, 16T05, 16E65, 16S37, 16W50 Let $G$ be a group coacting on an Artin-Schelter regular algebra $A$ homogeneously and inner-faithfully. When the identity component $A_e$ is also Artin-Schelter regular, providing a generalization of the Shephard-Todd-Chevalley Theorem, we say that $G$ is a dual reflection group for $A$. We give two examples of dual reflection groups of order 16, and study algebraic and geometric properties of three associated Artin-Schelter regular algebras of dimension four. |
| title | Some Artin-Schelter Regular Algebras From Dual Reflection Groups and their Geometry |
| topic | Rings and Algebras Quantum Algebra 16S38, 16W22, 16T05, 16E65, 16S37, 16W50 |
| url | https://arxiv.org/abs/2410.08959 |