Non-compact quantum groups arising from Heisenberg type Lie bialgebras
| dc.creator | Kahng, Byung-Jay | |
| dc.date | 1998-04-03 | |
| dc.date | 1999-10-08 | |
| dc.date.accessioned | 2026-07-07T05:24:18Z | |
| dc.date.available | 2026-07-07T05:24:18Z | |
| dc.description | The dual Lie bialgebra of a certain ``quasitriangular'' Lie bialgebra structure on the Heisenberg Lie algebra determines a (non-compact) Poisson--Lie group G. The compatible Poisson bracket on G is non-linear, but it can still be realized as a ``cocycle perturbation'' of the linear Poisson bracket. We construct a certain twisted group C*-algebra A, which is shown to be a strict deformation quantization of G. Motivated by the data at the Poisson (classical) level, we then construct on A its locally compact quantum group structures: comultiplication, counit, antipode and Haar weight, as well as its associated multiplicative unitary operator. We also find a quasitriangular ``quantum universal R-matrix'' type operator for A, which agrees well with the quasitriangularity at the Lie bialgebra level. | |
| dc.description | AMS LaTeX (36 pages), Revised version of previous math.OA9804019; to appear in J. Operator Theory | |
| dc.identifier | https://arxiv.org/abs/math/9804019 | |
| dc.identifier | http://arxiv.org/abs/math/9804019 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76788 | |
| dc.subject | Operator Algebras | |
| dc.subject | Quantum Algebra | |
| dc.subject | 46L87 81R50 22D25 | |
| dc.title | Non-compact quantum groups arising from Heisenberg type Lie bialgebras | |
| dc.type | text |