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Nonsmooth Calabi-Yau structures for algebras and coalgebras

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arxiv 2502.12162 v2 pith:SA7VTHEH submitted 2025-02-18 math.RA math.AGmath.ATmath.KTmath.RT

Nonsmooth Calabi-Yau structures for algebras and coalgebras

Matt Booth , Joseph Chuang , Andrey Lazarev This is my paper
classification math.RA math.AGmath.ATmath.KTmath.RT
keywords algebrascalabi-yaudualgeneralisedkoszulapplicationassumecharacterisation
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We show that generalised Calabi-Yau dg (co)algebras are Koszul dual to generalised symmetric dg (co)algebras, without needing to assume any smoothness or properness hypotheses. Similarly, we show that Gorenstein and Frobenius are Koszul dual properties. As an application, we give a new characterisation of Poincar\'e duality spaces, which extends a theorem of F\'elix- Halperin-Thomas to the non-simply connected setting.

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  1. Duality for graded Lie algebras

    math.QA 2026-01 accept novelty 7.0

    For a finite-dimensional graded Lie algebra, the dualizing complex of its enveloping algebra is one-dimensional with action by the supertrace of the adjoint representation; unimodular algebras thus have Calabi-Yau der...