Basic quasi-Hopf algebras over cyclic groups

Let m be a positive integer, not divisible by 2, 3, 5, 7. We generalize the classification of basic quasi-Hopf algebras over cyclic groups of prime order given in Etingof and Gelaki (2006) [11] to the case of cyclic groups of order in. To this end, we introduce a family of non-semisimple radically graded quasi-Hopf algebras A(H, s), constructed as subalgebras of Hopf algebras twisted by a quasi-Hopf twist, which are not twist equivalent to Hopf algebras. Any basic quasi-Hopf algebra over a cyclic group of order in is either semisimple, or is twist equivalent to a Hopf algebra or a quasi-Hopf algebra of type A(H, s). (C) 2010 Elsevier Inc. All rights reserved.