Duality Features of Left Hopf Algebroids

Authors: Sophie Chemla Fabio Gavarini Niels Kowalzig

Publish Date: 2016/03/04

Volume: 19, Issue: 4, Pages: 913-941

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Abstract

We explore special features of the pair U ∗U ∗ formed by the right and left dual over a left bialgebroid U in case the bialgebroid is in particular a left Hopf algebroid It turns out that there exists a bialgebroid morphism S ∗ from one dual to another that extends the construction of the antipode on the dual of a Hopf algebra and which is an isomorphism if U is both a left and right Hopf algebroid This structure is derived from Phùng’s categorical equivalence between left and right comodules over U without the need of a Hopf algebroid antipode a result which we review and extend In the applications we illustrate the difference between this construction and those involving antipodes and also deal with dualising modules and their quantisations

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