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Power sum elements in
the $G_2$ skein algebra
Bodie Beaumont-Gould, Erik Brodsky, Vijay Higgins, Alaina Hogan, Joseph M Melby and Joshua Piazza |
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Algebraic & Geometric Topology 25 (2025) 2477–2505
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Abstract |
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We study the skein algebras of surfaces associated to the exceptional Lie group , using Kuperberg webs. We identify two 2-variable polynomials, and , and use threading operations along knots to construct a family of central elements in the skein algebra of a surface, , when the quantum parameter is a root of unity. We verify these elements are central using elementary skein-theoretic arguments. We also obtain a result about the uniqueness of the so-called transparent polynomials and . Our methods involve a detailed study of the skein modules of the annulus and the twice-marked annulus. |
Keywords
skein algebras of surfaces, Kuperberg webs, power sum
polynomials
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Mathematical Subject Classification
Primary: 57K31
Secondary: 17B37
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References |
Publication
Received: 22 January 2024
Revised: 15 May 2024
Accepted: 5 June 2024
Published: 11 August 2025
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Authors |
| Bodie Beaumont-Gould | |
| Department of Mathematics Lewis and Clark College Portland, OR United States |
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| Erik Brodsky | |
| Department of Mathematics Michigan State University East Lansing, MI United States |
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| Vijay Higgins | |
| Department of Mathematics Michigan State University East Lansing, MI United States |
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| Alaina Hogan | |
| Department of Mathematics Grand Valley State University Allendale, MI United States |
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| Joseph M Melby | |
| Department of Mathematics Michigan State University East Lansing, MI United States |
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| Joshua Piazza | |
| Department of Mathematics and
Computer Science Wheaton College Wheaton, IL United States |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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