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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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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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.