A quasi-Hopf algebra for the triplet vertex operator algebra

Creutzig T, Gainutdinov AM, Runkel I (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Communications in Contemporary Mathematics World Scientific Publishing

Book Volume: 22

Article Number: 1950024

Journal Issue: 3

DOI: 10.1142/S021919971950024X

Abstract

We give a new factorizable ribbon quasi-Hopf algebra U, whose underlying algebra is that of the restricted quantum group for sa(2) at a 2pth root of unity. The representation category of U is conjecturally ribbon equivalent to that of the triplet vertex operator algebra (VOA) (p). We obtain U 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 a(p), and our construction is parallel to extending a(p) to (p). We illustrate the procedure in the simpler example of passing from the Hopf algebra for the group algebra a'a to a quasi-Hopf algebra for a'a;2p, which corresponds to passing from the Heisenberg VOA to a lattice extension.

Authors with CRIS profile

Thomas Creutzig

Involved external institutions

University of Alberta CA Canada (CA) François Rabelais University Tours FR France (FR) Universität Hamburg (UHH) DE Germany (DE)

How to cite

APA:

Creutzig, T., Gainutdinov, A.M., & Runkel, I. (2020). A quasi-Hopf algebra for the triplet vertex operator algebra. Communications in Contemporary Mathematics, 22(3). https://doi.org/10.1142/S021919971950024X

MLA:

Creutzig, Thomas, Azat M. Gainutdinov, and Ingo Runkel. "A quasi-Hopf algebra for the triplet vertex operator algebra." Communications in Contemporary Mathematics 22.3 (2020).

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