Frayed Demazure weaves yield Poisson-compatible cluster structures on Bott-Samelson charts whose transitions are rational quasi-cluster morphisms, with mutation sequences related to Ménard's open Richardson seeds.
Quantum cluster algebras.Advances in Mathematics, 195(2):405–455, 2005
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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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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.