On positivity of Kauffman bracket skein algebras of surfaces

TL;DR

This paper demonstrates that Chebyshev polynomials serve as fundamental components for constructing positive bases in Kauffman bracket skein algebras of surfaces, advancing understanding of their algebraic structure.

Contribution

It establishes the role of Chebyshev polynomials as building blocks for positive bases in skein algebras, a novel insight in the field.

Findings

Chebyshev polynomials form a basic block of positive bases

Provides a new perspective on the structure of skein algebras

Enhances understanding of positivity in algebraic bases

Abstract

We show that the Chebyshev polynomials form a basic block of any positive basis of the Kauffman bracket skein algebras of surfaces.