On positivity of Roger--Yang skein algebras
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917608797765632 |
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| author | Karuo, Hiroaki |
| author_facet | Karuo, Hiroaki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_01282 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On positivity of Roger--Yang skein algebras Karuo, Hiroaki Geometric Topology Quantum Algebra Rings and Algebras 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. |
| title | On positivity of Roger--Yang skein algebras |
| topic | Geometric Topology Quantum Algebra Rings and Algebras |
| url | https://arxiv.org/abs/2308.01282 |