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We give a new factorisable ribbon quasi-Hopf algebra U, whose underlyingalgebra is that of the restricted quantum group for sl(2) at a 2p'th root ofunity. The representation category of U is conjecturally ribbon-equivalent tothat of the triplet vertex operator algebra W(p). We obtain U via a simplecurrent extension from the unrolled restricted quantum group at the same rootof unity. The representation category of the unrolled quantum group isconjecturally 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 theprocedure in the simpler example of passing from the Hopf algebra for the groupalgebra CZ to a quasi-Hopf algebra for CZ_{2p}, which corresponds to passingfrom the Heisenberg vertex operator algebra to a lattice extension.

A quasi-Hopf algebra for the triplet vertex operator algebra