On positivity of Roger--Yang skein algebras
Geometric Topology
2024-03-12 v3 Quantum Algebra
Rings and Algebras
Abstract
We generalize the positivity conjecture on (Kauffman bracket) skein algebras to Roger--Yang skein algebras. To generalize it, we use explicit polynomials like Chebyshev polynomials of the first kind to give candidates of positive bases. Moreover, the polynomials form a lower bound in the sense of [L\^e18] and [LTY21]. We also discuss a relation between the polynomials and the centers of Roger--Yang skein algebras when the quantum parameter is a complex root of unity.
Keywords
Cite
@article{arxiv.2308.01282,
title = {On positivity of Roger--Yang skein algebras},
author = {Hiroaki Karuo},
journal= {arXiv preprint arXiv:2308.01282},
year = {2024}
}
Comments
13 pages, the finial version