New Modular Hopf Algebras related to rational $k$ $\widehat {sl(2)}$
| dc.creator | Ramgoolam, Sanjaye | |
| dc.date | 1993-01-29 | |
| dc.date | 1993-02-18 | |
| dc.date.accessioned | 2026-07-07T09:01:07Z | |
| dc.date.available | 2026-07-07T09:01:07Z | |
| dc.description | We show that the Hopf link invariants for an appropriate set of finite dimensional representations of $ U_q SL(2)$ are identical, up to overall normalisation, to the modular S matrix of Kac and Wakimoto for rational $k$ $\widehat {sl(2)}$ representations. We use this observation to construct new modular Hopf algebras, for any root of unity $q=e^{-iπm/r}$, obtained by taking appropriate quotients of $U_q SL(2)$, that give rise to 3-manifold invariants according to the approach of Reshetikin and Turaev. The phase factor correcting for the `framing anomaly' in these invariants is equal to $ e^{- {{i π} \over 4} ({ {3k} \over {k+2}})}$, an analytic continuation of the anomaly at integer $k$. As expected, the Verlinde formula gives fusion rule multiplicities in agreement with the modular Hopf algebras. This leads to a proposal, for $(k+2)=r/m$ rational with an odd denominator, for a set of $\widehat {sl(2)}$ representations obtained by dropping some of the highest weight representations in the Kac-Wakimoto set and replacing them with lowest weight representations. For this set of representations the Verlinde formula gives non-negative integer fusion rule multiplicities. We discuss the consistency of the truncation to highest and lowest weight representations in conformal field theory. | |
| dc.description | 30 pages (minor typos corrected, refs added) | |
| dc.identifier | https://arxiv.org/abs/hep-th/9301121 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9301121 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/148220 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Quantum Algebra | |
| dc.title | New Modular Hopf Algebras related to rational $k$ $\widehat {sl(2)}$ | |
| dc.type | text |