Liftings of pointed coradically graded coquasi-Hopf algebras

Compute all liftings (i.e., deformations yielding non-graded coquasi-Hopf algebras with the same associated graded) of the pointed coradically graded coquasi-Hopf algebras classified in HLYY, thereby completing the classification of finite pointed tensor categories with abelian groups of invertible objects.

Background

Pointed tensor categories with abelian groups of invertible objects have been classified at the graded level, with finite Nichols algebras arising only for trivializable 3-cocycles. To fully classify such categories up to equivalence, one must compute all possible liftings of the graded coquasi-Hopf algebras, potentially leveraging de-equivariantization and cocycle deformation methods analogous to the Hopf algebra case.