The Larson-Sweedler theorem for multiplier Hopf algebras
| dc.creator | Van Daele, Alfons | |
| dc.creator | Wang, Shuanhong | |
| dc.date | 2004-08-17 | |
| dc.date.accessioned | 2026-07-07T05:11:19Z | |
| dc.date.available | 2026-07-07T05:11:19Z | |
| dc.description | Any finite-dimensional Hopf algebra has a left and a right integral. Conversely, Larsen and Sweedler showed that, if a finite-dimensional algebra with identity and a comultiplication with counit has a faithful left integral, it has to be a Hopf algebra. In this paper, we generalize this result to possibly infinite-dimensional algebras, with or without identity. We have to leave the setting of Hopf algebras and work with multiplier Hopf algebras. Moreover, whereas in the finite-dimensional case, there is a complete symmetry between the bialgebra and its dual, this is no longer the case in infinite dimensions. Therefore we consider a direct version (with integrals) and a dual version (with cointegrals) of the Larson-Sweedler theorem. We also add some results about the antipode. Furthermore, in the process of this paper, we obtain a new approach to multiplier Hopf algebras with integrals. | |
| dc.identifier | https://arxiv.org/abs/math/0408218 | |
| dc.identifier | http://arxiv.org/abs/math/0408218 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72199 | |
| dc.subject | Quantum Algebra | |
| dc.title | The Larson-Sweedler theorem for multiplier Hopf algebras | |
| dc.type | text |