Work

Power sum elements in the G2 skein algebra

Year: 2025

Type: article

Abstract: We study the skein algebras of surfaces associated to the exceptional Lie group G 2 , using Kuperberg webs.We identify two 2-variable polynomials, P n .x;y/ and Q n .x;y/, and use threading operations along knots to construct a family of central elements in the G 2 skein algebra of a surface, S G 2 q .†/, when the quantum parameter q is a 2n th 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 P n and Q n .Our methods involve a detailed study of the skein modules of the annulus and the twice-marked annulus.

Source: Algebraic & Geometric Topology

DOI: 10.2140/agt.2025.25.2477

Authors: Bodie Beaumont-Gould, Erik Brodsky, Vijay Higgins, Alaina Hogan, Joseph M Melby, Joshua Piazza

Institutions: Lewis & Clark College, Michigan State University, Grand Valley State University, Wheaton College - Illinois

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: National Science Foundation, Michigan State University, College of Engineering, Michigan State University

Award: RTG: Algebraic and Geometric Topology at Michigan State