Frobenius Algebras Derived from the Kauffman Bracket Skein Algebra

TL;DR

This paper constructs Frobenius algebras from skein modules of specific surfaces at roots of unity, advancing the algebraic understanding of quantum invariants in topology.

Contribution

It introduces a method to derive Frobenius algebras from skein modules of certain surfaces at roots of unity, expanding the algebraic framework in quantum topology.

Findings

Frobenius algebras constructed from skein modules of surfaces.

Analysis at 2N-th roots of unity with N odd and ≥ 3.

Provides new algebraic tools for quantum topology studies.

Abstract

In this paper we study the skein modules of the surfaces, $\Sigma_{i,j}$ $(i,j)\in \{(0,2),(0,3),(1,0),(1,1)\}$ at $2N$-th roots of unity where $N\geq 3$ is an odd counting number and construct Frobenius algebras from them.