Equivariant spectral triples and Poincaré duality for $SU_q(2)$
| dc.creator | Chakraborty, Partha Sarathi | |
| dc.creator | Pal, Arupkumar | |
| dc.date | 2002-11-23 | |
| dc.date | 2008-11-26 | |
| dc.date.accessioned | 2026-07-07T10:38:18Z | |
| dc.date.available | 2026-07-07T10:38:18Z | |
| dc.description | Let $\mathcal{A}$ be the $C^*$-algebra associated with $SU_q(2)$, $π$ be the representation by left multiplication on the $L_2$ space of the Haar state and let $D$ be the equivariant Dirac operator for this representation constructed by the authors earlier. We prove in this article that there is no operator other than the scalars in the commutant $π(\cla)'$ that has bounded commutator with $D$. This implies that the equivariant spectral triple under consideration does not admit a rational Poincaré dual in the sense of Moscovici, which in particular means that this spectral triple does not extend to a $K$-homology fundamental class for $SU_q(2)$. We also show that a minor modification of this equivariant spectral triple gives a fundamental class and thus implements Poincaré duality. | |
| dc.description | v2: main result strengthened, a new section added, title changed; 21 pages, LaTeX v1: 9 pages, Latex2e | |
| dc.identifier | https://arxiv.org/abs/math/0211367 | |
| dc.identifier | http://arxiv.org/abs/math/0211367 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/180674 | |
| dc.subject | Operator Algebras | |
| dc.subject | Quantum Algebra | |
| dc.subject | 58B34, 46L87, 19K33 | |
| dc.title | Equivariant spectral triples and Poincaré duality for $SU_q(2)$ | |
| dc.type | text |