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arXiv · 2312.06148

Matrix Formulae and Skein Relations for Quasi-Cluster Algebras

Cody Gilbert·McCleary Philbin·Kayla Wright
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Abstract

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.

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Cody Gilbert, McCleary Philbin, Kayla Wright. 2026-02-27. Matrix Formulae and Skein Relations for Quasi-Cluster Algebras. https://doi.org/10.3842/sigma.2026.019

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