English

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