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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Modified c- and g-vectors of the Markov quiver exhibit a fractal structure via linear isomorphisms and admit recursive formulas parameterized by coprime integers, which classify the complement of the G-fan.
The authors prove that proper relative Ginzburg algebras yield an additive Λ-cluster algebra structure via negative extensions in Higgs categories, providing an additive view of the monoidal Λ-invariant for untwisted simply-laced types.
Extends Muller-Speyer by constructing extremal matchings via height functions on almost perfect matchings of plabic graphs and proving coverage of all boundary conditions.
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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Fractal phenomenon in $c$- and $g$-vectors of the Markov quiver
Modified c- and g-vectors of the Markov quiver exhibit a fractal structure via linear isomorphisms and admit recursive formulas parameterized by coprime integers, which classify the complement of the G-fan.
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Additive categorification of the monoidal $\Lambda$-invariant
The authors prove that proper relative Ginzburg algebras yield an additive Λ-cluster algebra structure via negative extensions in Higgs categories, providing an additive view of the monoidal Λ-invariant for untwisted simply-laced types.
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Extremal Matchings and Height Functions
Extends Muller-Speyer by constructing extremal matchings via height functions on almost perfect matchings of plabic graphs and proving coverage of all boundary conditions.