A quasi-Hopf algebra for the triplet vertex operator algebra - Creutzig, Thomas; Gainutdinov, Azat M.; Runkel, Ingo (Communications in Contemporary Mathematics, 2020)
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.
CRIS-Team Scopus Importer:2024-06-24
Keywords: braided tensor categories; logarithmic modules; quantum groups; quasi-Hopf algebras; Vertex operator algebras