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Auteurs principaux: Lawrence, Justin, Rouse, Nicholas, Williams, Ben
Format: Preprint
Publié: 2025
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Accès en ligne:https://arxiv.org/abs/2510.25149
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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
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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