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].
Tipologia: | Articolo su rivista | |
Citazione: | 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]. | |
URL: | http://link.springer.com/article/10.1007%2Fs10468-016-9604-9 | |
IF: | Con Impact Factor ISI | |
Lingua: | English | |
Settore Scientifico Disciplinare: | Settore MAT/02 - Algebra | |
Revisione (peer review): | Esperti anonimi | |
Tipo: | Articolo | |
Rilevanza: | Rilevanza internazionale | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s10468-016-9604-9 | |
Stato di pubblicazione: | Pubblicato | |
Data di pubblicazione: | ago-2016 | |
Titolo: | Duality Features of Left Hopf Algebroids | |
Autori: | ||
Autori: | Chemla, S; Gavarini, F; Kowalzig, N | |
Appare nelle tipologie: | 01 - Articolo su rivista |
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DualH-STA - offprint.pdf | This is the PDF file of the Authors' own offprint copy - i.e., the Editor's printed version | N/A | Copyright dell'editore | Administrator Richiedi una copia |
DualH22 - CORR - ref.pdf | This is the PDF file of the Authors' own post-print version | N/A | Copyright dell'editore | Open Access Visualizza/Apri |