The authors define extra slow Tamari lattices on faithfully balanced tableaux, prove they are lattices that are semidistributive, trim, polygonal and congruence uniform, describe their join-irreducibles via three-color roots, and obtain enumerative results.
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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.
Generalizes Etingof-Eu graded Euler characteristic approach to higher preprojective algebras and shows that for 2-representation finite algebras from type A tensor products, the full graded Hochschild (co)homology and cyclic homology follow from the center and HH_0.
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The extra slow Tamari lattice
The authors define extra slow Tamari lattices on faithfully balanced tableaux, prove they are lattices that are semidistributive, trim, polygonal and congruence uniform, describe their join-irreducibles via three-color roots, and obtain enumerative results.
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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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Hochschild (co)homology and cyclic homology via a graded Euler characteristic with applications to higher preprojective algebras
Generalizes Etingof-Eu graded Euler characteristic approach to higher preprojective algebras and shows that for 2-representation finite algebras from type A tensor products, the full graded Hochschild (co)homology and cyclic homology follow from the center and HH_0.