Equivariant spectral triples for $SU_q(\ell+1)$ and the odd dimensional quantum spheres
| dc.creator | Chakraborty, Partha Sarathi | |
| dc.creator | Pal, Arupkumar | |
| dc.date | 2005-03-29 | |
| dc.date | 2005-04-21 | |
| dc.date.accessioned | 2026-07-07T05:18:36Z | |
| dc.date.available | 2026-07-07T05:18:36Z | |
| dc.description | We formulate the notion of equivariance of an operator with respect to a covariant representation of a C^*-dynamical system. We then use a combinatorial technique used by the authors earlier in characterizing spectral triples for SU_q(2) to investigate equivariant spectral triples for two classes of spaces: the quantum groups SU_q(\ell+1) for \ell>1, and the odd dimensional quantum spheres S_q^{2\ell+1} of Vaksman & Soibelman. In the former case, a precise characterization of the sign and the singular values of an equivariant Dirac operator acting on the L_2 space is obtained. Using this, we then exhibit equivariant Dirac operators with nontrivial sign on direct sums of multiple copies of the L_2 space. In the latter case, viewing S_q^{2\ell+1} as a homogeneous space for SU_q(\ell+1), we give a complete characterization of equivariant Dirac operators, and also produce an optimal family of spectral triples with nontrivial K-homology class. | |
| dc.description | v2: some small mistakes resulting from an error in an expression for CG coefficient corrected; three references added. v1: LaTeX2e, uses xy-pic and eepic | |
| dc.identifier | https://arxiv.org/abs/math/0503689 | |
| dc.identifier | http://arxiv.org/abs/math/0503689 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74719 | |
| dc.subject | Quantum Algebra | |
| dc.subject | K-Theory and Homology | |
| dc.subject | Operator Algebras | |
| dc.subject | 58B34, 46L87, 19K33 | |
| dc.title | Equivariant spectral triples for $SU_q(\ell+1)$ and the odd dimensional quantum spheres | |
| dc.type | text |