Two-sided (two-cosided) Hopf modules and Doi-Hopf modules for quasi-Hopf algebras
| dc.creator | Bulacu, D. | |
| dc.creator | Caenepeel, S. | |
| dc.date | 2002-11-27 | |
| dc.date.accessioned | 2026-07-07T04:53:21Z | |
| dc.date.available | 2026-07-07T04:53:21Z | |
| dc.description | Let $H$ be a finite dimensional quasi-Hopf algebra over a field $k$ and ${\mathfrak A}$ a right $H$-comodule algebra in the sense of Hausser and Nill. We first show that on the $k$-vector space ${\mathfrak A}\ot H^*$ we can define an algebra structure, denoted by ${\mathfrak A}\ovsm H^*$, in the monoidal category of left $H$-modules (i.e. ${\mathfrak A}\ovsm H^*$ is an $H$-module algebra. Then we will prove that the category of two-sided $({\mathfrak A}, H)$-bimodules $\hba $ is isomorphic to the category of relative $({\mathfrak A}\ovsm H^*, H^*)$-Hopf modules, as introduced in by Hausser and Nill. In the particular case where ${\mathfrak A}=H$, we will obtain a result announced by Nill. We will also introduce the categories of Doi-Hopf modules and two-sided two-cosided Hopf modules and we will show that they are in certain situations isomorphic to module categories. | |
| dc.description | 31 pages | |
| dc.identifier | https://arxiv.org/abs/math/0211430 | |
| dc.identifier | http://arxiv.org/abs/math/0211430 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65814 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16W30 | |
| dc.title | Two-sided (two-cosided) Hopf modules and Doi-Hopf modules for quasi-Hopf algebras | |
| dc.type | text |