Basic quasi-Hopf algebras of dimension n^3

Details Basic quasi-Hopf algebras of dimension n^3 Basic quasi-Hopf algebras of dimension n^3

2004-02-10

arxiv.org/abs/math/0402159v3

Mathematics

Quantum Algebra

8 pages, latex; minor corrections. The paper will appear in Journal of Pure and Applied Algebra

Scientific paper

It is shown in math.QA/0310253 that a finite dimensional quasi-Hopf algebra over the complex numbers with radical of codimension 2 is twist equivalent to a Nichols Hopf algebra, or to a lifting of one of four special quasi-Hopf algebras of dimensions 2, 8, 8, and 32. The purpose of this paper is to construct new finite dimensional basic quasi-Hopf algebras A(q) of dimension n^3, n>2, parametrized by primitive roots of unity q of order n^2, with radical of codimension n, which generalize the construction of the basic quasi-Hopf algebras of dimension 8 given in math.QA/0310253. These quasi-Hopf algebras are not twist equivalent to a Hopf algebra, and may be regarded as quasi-Hopf analogs of Taft Hopf algebras. By math.QA/0301027, our construction is equivalent to the construction of new finite tensor categories whose simple objects form a cyclic group of order n, and which are not tensor equivalent to a representation category of a Hopf algebra. In a later publication we plan to use our construction to classify finite tensor categories whose simple objects form a cyclic group of prime order n. We also prove that if H is a finite dimensional radically graded quasi-Hopf algebra with H[0]=(C[\Z/n\Z],\Phi), where n is prime and \Phi is a nontrivial associator, such that H[1] is a free left module over H[0] of rank 1 (it is always free) then H is isomorphic to A(q).

Affiliated with

Also associated with

No associations

Rating

Basic quasi-Hopf algebras of dimension n^3 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Basic quasi-Hopf algebras of dimension n^3, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Basic quasi-Hopf algebras of dimension n^3 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-168067