For polygonal surfaces, the localized stated SL_n-skein algebra equals the associated quantum cluster algebra, producing a rotation-invariant basis.
arXiv preprint arXiv:2303.08082 , year=
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SL(n) skein algebra of the twice punctured sphere is a commutative polynomial algebra in n-1 explicit crossing-free web generators for generic q.
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Quantum cluster algebra realization for stated ${\rm SL}_n$-skein algebras and rotation-invariant bases for polygons
For polygonal surfaces, the localized stated SL_n-skein algebra equals the associated quantum cluster algebra, producing a rotation-invariant basis.
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Monomial web basis for the SL(N) skein algebra of the twice punctured sphere
SL(n) skein algebra of the twice punctured sphere is a commutative polynomial algebra in n-1 explicit crossing-free web generators for generic q.