For polygonal surfaces, the localized stated SL_n-skein algebra equals the associated quantum cluster algebra, producing a rotation-invariant basis.
Bracelets bases are theta bases
5 Pith papers cite this work. Polarity classification is still indexing.
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Multiple equivalent combinatorial expansion formulas are given for generalized cluster algebras from arcs on punctured orbifolds, generalizing prior surface and orbifold cases.
A birational Weyl group action on the cluster A_n-quiver has as its Poisson invariants exactly the formal geodesic functions (matrix entries), yielding transitive Hamiltonian reductions on the geometric leaf and an even/odd parity dichotomy for cluster DT-transformations.
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.
Constructs quantized trace-of-monodromy via Bonahon-Wong maps and verifies Teschner recursion plus strong commutation for disjoint loops in Chekhov-Fock quantum Teichmüller theory.
citing papers explorer
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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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Cluster Expansions from Punctured Orbifolds
Multiple equivalent combinatorial expansion formulas are given for generalized cluster algebras from arcs on punctured orbifolds, generalizing prior surface and orbifold cases.
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Birational Weyl Group Action on the Symplectic Groupoid and Cluster Algebras
A birational Weyl group action on the cluster A_n-quiver has as its Poisson invariants exactly the formal geodesic functions (matrix entries), yielding transitive Hamiltonian reductions on the geometric leaf and an even/odd parity dichotomy for cluster DT-transformations.
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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.
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Quantized Geodesic Lengths for Teichm\"uller Spaces: Algebraic Aspects
Constructs quantized trace-of-monodromy via Bonahon-Wong maps and verifies Teschner recursion plus strong commutation for disjoint loops in Chekhov-Fock quantum Teichmüller theory.