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- Thomas Creutzig
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1, Canada
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- Azat M. Gainutdinov
- Institut Denis Poisson, CNRS, Université de Tours, Université d’Orléans, Parc de Grammont, 37200 Tours, France
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- Ingo Runkel
- Fachbereich Mathematik, Universität Hamburg, Bundesstr, 55, 20146 Hamburg, Germany
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説明
<jats:p> 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. </jats:p>
収録刊行物
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- Communications in Contemporary Mathematics
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Communications in Contemporary Mathematics 22 (03), 1950024-, 2019-04-11
World Scientific Pub Co Pte Ltd