HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

A quasi-Hopf algebra for the triplet vertex operator algebra

Abstract : We give a new factorisable ribbon quasi-Hopf algebra U , whose underlying algebra is that of the restricted quantum group for sℓ(2) at a 2p'th root of unity. The representation category of U is conjecturally ribbon-equivalent to that of the triplet vertex operator algebra W(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 vertex operator algebra M(p), and our construction is parallel to extending M(p) to W(p). We illustrate the procedure in the simpler example of passing from the Hopf algebra for the group algebra CZ to a quasi-Hopf algebra for CZ_{2p}, which corresponds to passing from the Heisenberg vertex operator algebra to a lattice extension.
Complete list of metadata

Cited literature [113 references]  Display  Hide  Download

Contributor : Sandrine Renard-Riccetti Connect in order to contact the contributor
Submitted on : Thursday, October 24, 2019 - 3:21:39 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:35 PM
Long-term archiving on: : Saturday, January 25, 2020 - 4:45:47 PM


Files produced by the author(s)




Thomas Creutzig, Azat Gainutdinov, Ingo Runkel. A quasi-Hopf algebra for the triplet vertex operator algebra. Communications in Contemporary Mathematics, World Scientific Publishing, 2019, pp.1950024. ⟨10.1142/S021919971950024X⟩. ⟨hal-02331895⟩



Record views


Files downloads