A quasi-Hopf algebra for the triplet vertex operator algebra
- Creutzig, Thomas Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1, Canada
- Gainutdinov, Azat M. Fachbereich Mathematik, Universität Hamburg, Bundesstr, 55, 20146 Hamburg, Germany
- Runkel, Ingo Fachbereich Mathematik, Universität Hamburg, Bundesstr, 55, 20146 Hamburg, Germany
- 2019-4-11
Published in:
- Communications in Contemporary Mathematics. - World Scientific Pub Co Pte Lt. - 2019, vol. 22, no. 03, p. 1950024
English
We give a new factorizable ribbon quasi-Hopf algebra [Formula: see text], whose underlying algebra is that of the restricted quantum group for [Formula: see text] at a [Formula: see text]th root of unity. The representation category of [Formula: see text] is conjecturally ribbon equivalent to that of the triplet vertex operator algebra (VOA) [Formula: see text]. We obtain [Formula: see text] via a simple current extension from the unrolled restricted quantum group at the same root of unity. The representation category of the unrolled quantum group is conjecturally equivalent to that of the singlet VOA [Formula: see text], and our construction is parallel to extending [Formula: see text] to [Formula: see text]. We illustrate the procedure in the simpler example of passing from the Hopf algebra for the group algebra [Formula: see text] to a quasi-Hopf algebra for [Formula: see text], which corresponds to passing from the Heisenberg VOA to a lattice extension.
- Language
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- English
- Open access status
- green
- Identifiers
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- DOI 10.1142/s021919971950024x
- ISSN 0219-1997
- Persistent URL
- https://sonar.rero.ch/global/documents/121405
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