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Singular Hochschild cohomology via the singularity category

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arxiv 1809.05121 v10 pith:5BOZ4XNO submitted 2018-09-13 math.RT math.AGmath.KT

Bernhard Keller This is my paper · ORCID
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abstract

We show that for a noetherian algebra $A$ whose bounded dg derived category is smooth, the singular Hochschild cohomology (=Tate--Hochschild cohomology) is isomorphic, as a graded algebra, to the Hochschild cohomology of the dg singularity category of $A$. The existence of such an isomorphism is suggested by recent work of Zhengfang Wang.

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  1. Monoidal structures arising from $B_\infty$-algebras with applications to Hopf algebras

    math.RT 2026-08 conditional novelty 8.0 of 10

    A B-infinity structure on an algebra gives a monoidal tensor product on the derived category of right modules, and for Hopf algebras this produces an algebraic proof of the Benson-Krause monoidal equivalence.

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