The Kauffman skein algebra of the torus
Hugh Morton, Alexander Pokorny, Peter Samuelson
TL;DR
This paper presents a detailed algebraic description of the Kauffman skein algebra of the torus, extending known results and establishing compatibility with existing frameworks for related skein algebras.
Contribution
It provides a new presentation of the Kauffman (BMW) skein algebra of the torus and shows its compatibility with Frohman-Gelca's description of the Temperley-Lieb skein algebra.
Findings
New algebraic presentation of the Kauffman skein algebra of the torus
Compatibility established with Frohman-Gelca's Temperley-Lieb skein algebra
Extension of known skein algebra computations to type BCD analogues
Abstract
We give a presentation of the Kauffman (BMW) skein algebra of the torus, which is the "type BCD" analogue of the Homflypt skein algebra of torus which was computed by the first and third authors. In the appendix we show this presentation is compatible with the Frohman-Gelca description of the Kauffman bracket (Temperley-Lieb) skein algebra of the torus [FG00].
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology