Compact and discrete subgroups of algebraic quantum groups I
| dc.creator | Landstad, M. B. | |
| dc.creator | Van Daele, A. | |
| dc.date | 2007-02-15 | |
| dc.date | 2007-04-12 | |
| dc.date.accessioned | 2026-07-07T07:56:16Z | |
| dc.date.available | 2026-07-07T07:56:16Z | |
| dc.description | Let $G$ be a locally compact group. Consider the C$^*$-algebra $C_0(G)$ of continuous complex functions on $G$, tending to 0 at infinity. The product in $G$ gives rise to a coproduct $Δ_G$ on the C$^*$-algebra $C_0(G)$. A locally compact {\it quantum} group is a pair $(A,Δ)$ of a C$^*$-algebra $A$ with a coproduct $Δ$ on $A$, satisfying certain conditions. The definition guarantees that the pair $(C_0(G),Δ_G)$ is a locally compact quantum group and that conversely, every locally compact quantum group $(A,Δ)$ is of this form when the underlying C$^*$-algebra $A$ is abelian. Assume now that $G$ is a locally compact group with a compact open subgroup $K$. The algebra of complex functions on $G$ of {\it polynomial type} is a dense multiplier Hopf $^*$-algebra with positive integrals (i.e. an algebraic quantum group}. The characteristic function of $K$ is a group-like projection in this algebraic quantum group. In this paper, we study group-like projections in an arbitrary algebraic quantum group. We find several associated objects that generalize the classical objects associated to a compact open subgroup of a locally compact group. | |
| dc.identifier | https://arxiv.org/abs/math/0702458 | |
| dc.identifier | http://arxiv.org/abs/math/0702458 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127248 | |
| dc.subject | Operator Algebras | |
| dc.subject | Rings and Algebras | |
| dc.subject | 20N20; 16W30; 81R50 | |
| dc.title | Compact and discrete subgroups of algebraic quantum groups I | |
| dc.type | text |