Basic quasi-Hopf algebras over cyclic groups

By I. Angiono. 2009

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Abstract 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 m. 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 m is either semisimple, or is twist equivalent to a Hopf algebra or a quasi-Hopf algebra of type A ( H , s ) .

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/57eaa709ff51c0d762611ea074c0e434162658e1