A quasi-Hopf algebra for the triplet vertex operator algebra

Understand

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).