On positivity of Roger--Yang skein algebras
arXiv:2308.01282 · doi:10.1016/j.jalgebra.2024.01.045
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 [Lê18] 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.
arXiv comment13 pages, the finial version
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