Finite dimensional quasi-Hopf algebras with radical of codimension 2

Simple item page
dc.creatorEtingof, Pavel
dc.creatorGelaki, Shlomo
dc.date2003-10-16
dc.date2003-10-20
dc.date.accessioned2026-07-07T05:01:58Z
dc.date.available2026-07-07T05:01:58Z
dc.descriptionIt is shown in math.QA/0301027 that a finite dimensional quasi-Hopf algebra with radical of codimension 1 is semisimple and 1-dimensional. On the other hand, there exist quasi-Hopf (in fact, Hopf) algebras, whose radical has codimension 2. Namely, it is known that these are exactly the Nichols Hopf algebras H_{2^n} of dimension 2^n, n\ge 1 (one for each value of n). The main result of this paper is that if H is a finite dimensional quasi-Hopf algebra over C with radical of codimension 2, then H is twist equivalent to a Nichols Hopf algebra H_{2^n}, n\ge 1, or to a lifting of one of the four special quasi-Hopf algebras H(2), H_+(8), H_-(8), H(32) of dimensions 2, 8, 8, and 32, defined in Section 3. As a corollary we obtain that any finite tensor category which has two invertible objects and no other simple object is equivalent to \Rep(H_{2^n}) for a unique n\ge 1, or to a deformation of the representation category of H(2), H_+(8), H_-(8), or H(32). As another corollary we prove that any nonsemisimple quasi-Hopf algebra of dimension 4 is twist equivalent to H_4.
dc.description9 pages, latex
dc.identifierhttps://arxiv.org/abs/math/0310253
dc.identifierhttp://arxiv.org/abs/math/0310253
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68883
dc.subjectQuantum Algebra
dc.titleFinite dimensional quasi-Hopf algebras with radical of codimension 2
dc.typetext

Files

Collections

arXiv