TL;DR
This paper establishes a twisted Poincaré duality for Hopf algebroids with bijective antipode, connecting it to Hochschild and Poisson dualities, thus extending duality concepts across algebraic and geometric structures.
Contribution
It proves a new twisted Poincaré duality for Hopf algebroids with bijective antipode, unifying algebraic and geometric dualities.
Findings
Recovered Hochschild twisted Poincaré duality of Van Den Bergh
Established Poisson twisted Poincaré duality for oriented Poisson manifolds
Extended duality concepts to Hopf algebroids with bijective antipode
Abstract
We prove a twisted Poincar\'e duality for (full) Hopf algebroids with bijective antipode. As an application, we recover the Hochschild twisted Poincar\'e duality of Van Den Bergh [VDB]. We also get a Poisson twisted Poincar\'e duality, which was already stated for oriented Poisson manifolds in [CLYZ].
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