Multiplier Hopf algebras imbedded in C$^*$-algebraic quantum groups
| dc.creator | De Commer, K. | |
| dc.creator | Van Daele, A. | |
| dc.date | 2006-11-28 | |
| dc.date | 2006-11-29 | |
| dc.date.accessioned | 2026-07-07T07:33:26Z | |
| dc.date.available | 2026-07-07T07:33:26Z | |
| dc.description | Let $(A,Δ)$ be a locally compact quantum group and $(A_0,Δ_0)$ a regular multiplier Hopf algebra. We show that if $(A_0,Δ_0)$ can in some sense be imbedded in $(A,Δ)$, then $A_0$ will inherit some of the analytic structure of $A$. Under certain conditions on the imbedding, we will be able to conclude that $(A_0,Δ_0)$ is actually an algebraic quantum group with a full analytic structure. The techniques used to show this, can be applied to obtain the analytic structure of a $^*$-algebraic quantum group {\it in a purely algebraic fashion}. Moreover, the {\it reason} that this analytic structure exists at all, is that the one-parameter groups, such as the modular group and the scaling group, are diagonizable. In particular, we will show that necessarily the scaling constant $μ$ of a $^*$-algebraic quantum group equals 1. This solves an open problem. | |
| dc.identifier | https://arxiv.org/abs/math/0611872 | |
| dc.identifier | http://arxiv.org/abs/math/0611872 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119458 | |
| dc.subject | Operator Algebras | |
| dc.subject | Rings and Algebras | |
| dc.title | Multiplier Hopf algebras imbedded in C$^*$-algebraic quantum groups | |
| dc.type | text |