Invariant integration theory on non-compact quantum spaces: Quantum (n,1)-matrix ball
| dc.creator | Kuersten, Klaus-Detlef | |
| dc.creator | Wagner, Elmar | |
| dc.date | 2003-05-27 | |
| dc.date.accessioned | 2026-07-07T04:58:18Z | |
| dc.date.available | 2026-07-07T04:58:18Z | |
| dc.description | An operator theoretic approach to invariant integration theory on non-compact quantum spaces is introduced on the example of the quantum (n,1)-matrix ball O_q(Mat_{n,1}). In order to prove the existence of an invariant integral, operator algebras are associated to O_q(Mat_{n,1}) which allow an interpretation as ``rapidly decreasing'' functions and as functions with compact support on the quantum (n,1)-matrix ball. It is shown that the invariant integral is given by a generalization of the quantum trace. If an operator representation of a first order differential calculus over the quantum space is known, then it can be extended to the operator algebras of integrable functions. Hilbert space representations of O_q(Mat_{n,1}) are investigated and classified. Some topological aspects concerning Hilbert space representations are discussed. | |
| dc.description | 35 pages | |
| dc.identifier | https://arxiv.org/abs/math/0305380 | |
| dc.identifier | http://arxiv.org/abs/math/0305380 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67585 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Operator Algebras | |
| dc.subject | 17B37; 47L60; 81R50 | |
| dc.title | Invariant integration theory on non-compact quantum spaces: Quantum (n,1)-matrix ball | |
| dc.type | text |