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arXiv · 2201.05361

Pivotality, twisted centres and the anti-double of a Hopf monad

Sebastian Halbig·Tony Zorman
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Abstract

Finite-dimensional Hopf algebras admit a correspondence between so-called pairs in involution, one-dimensional anti-Yetter--Drinfeld modules and algebra isomorphisms between the Drinfeld and anti-Drinfeld double. We extend it to general rigid monoidal categories and provide a monadic interpretation under the assumption that certain coends exist. Hereto we construct and study the anti-Drinfeld double of a Hopf monad. As an application the connection with the pivotality of Drinfeld centres and their underlying categories is discussed.

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Sebastian Halbig, Tony Zorman. 2022-01-14. Pivotality, twisted centres and the anti-double of a Hopf monad. https://arxiv.org/abs/2201.05361

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