Matrix Formulae and Skein Relations for Quasi-Cluster Algebras
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917299330482176 |
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| author | Gilbert, Cody Philbin, McCleary Wright, Kayla |
| author_facet | Gilbert, Cody Philbin, McCleary Wright, Kayla |
| contents | In this paper, we give matrix formulae for non-orientable surfaces that provide the Laurent expansion for quasi-cluster variables, generalizing the orientable surface matrix formulae by Musiker-Williams. We additionally use our matrix formulas to prove the skein relations for the elements in the quasi-cluster algebra associated to curves on the non-orientable surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_06148 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Matrix Formulae and Skein Relations for Quasi-Cluster Algebras Gilbert, Cody Philbin, McCleary Wright, Kayla Combinatorics Geometric Topology Rings and Algebras In this paper, we give matrix formulae for non-orientable surfaces that provide the Laurent expansion for quasi-cluster variables, generalizing the orientable surface matrix formulae by Musiker-Williams. We additionally use our matrix formulas to prove the skein relations for the elements in the quasi-cluster algebra associated to curves on the non-orientable surface. |
| title | Matrix Formulae and Skein Relations for Quasi-Cluster Algebras |
| topic | Combinatorics Geometric Topology Rings and Algebras |
| url | https://arxiv.org/abs/2312.06148 |