We explore special features of the pair (U (au),U (au)) 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 (au) 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 PhA(1)ng'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.

Chemla, S., Gavarini, F., Kowalzig, N. (2016). Duality Features of Left Hopf Algebroids. ALGEBRAS AND REPRESENTATION THEORY, 19(4), 913-941 [10.1007/s10468-016-9604-9].

Duality Features of Left Hopf Algebroids

GAVARINI, FABIO;Kowalzig, N.
2016-08-01

Abstract

We explore special features of the pair (U (au),U (au)) 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 (au) 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 PhA(1)ng'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.
ago-2016
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/02 - ALGEBRA
English
Con Impact Factor ISI
Hopf algebroids; Quantum groupoids; Duals; Dualising modules; (Co) module categories; Lie-Rinehart algebras
http://link.springer.com/article/10.1007%2Fs10468-016-9604-9
Chemla, S., Gavarini, F., Kowalzig, N. (2016). Duality Features of Left Hopf Algebroids. ALGEBRAS AND REPRESENTATION THEORY, 19(4), 913-941 [10.1007/s10468-016-9604-9].
Chemla, S; Gavarini, F; Kowalzig, N
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/168354
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