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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2510.25149 |
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| _version_ | 1866912675920871424 |
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| author | Lawrence, Justin Rouse, Nicholas Williams, Ben |
| author_facet | Lawrence, Justin Rouse, Nicholas Williams, Ben |
| contents | We give criteria to determine when a degree-2 Azumaya algebra with $C_2$-action over a dense open subvariety of a curve extends to the entire curve as an algebra with $C_2$-action. These consist of conditions for the extension of the algebra, combined with a new condition for the extension of the algebra with the action. The new condition is testable by computer algebra systems, and we explain how the result applies to the canonical components of the character varieties of certain hyperbolic knots with order-2 symmetries. We conclude by carrying out the calculations for different symmetries of the Figure-8 knot. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25149 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extending degree-2 Azumaya algebras with C2-actions and examples from character varieties of knot group Lawrence, Justin Rouse, Nicholas Williams, Ben Rings and Algebras Geometric Topology 16H05 (Primary) 57K31 (Secondary) We give criteria to determine when a degree-2 Azumaya algebra with $C_2$-action over a dense open subvariety of a curve extends to the entire curve as an algebra with $C_2$-action. These consist of conditions for the extension of the algebra, combined with a new condition for the extension of the algebra with the action. The new condition is testable by computer algebra systems, and we explain how the result applies to the canonical components of the character varieties of certain hyperbolic knots with order-2 symmetries. We conclude by carrying out the calculations for different symmetries of the Figure-8 knot. |
| title | Extending degree-2 Azumaya algebras with C2-actions and examples from character varieties of knot group |
| topic | Rings and Algebras Geometric Topology 16H05 (Primary) 57K31 (Secondary) |
| url | https://arxiv.org/abs/2510.25149 |