Biperfect Hopf Algebras

Details Biperfect Hopf Algebras Biperfect Hopf Algebras

1999-12-08

arxiv.org/abs/math/9912068v1

Mathematics

Quantum Algebra

5 pages, latex

Scientific paper

Recall that a finite group is called perfect if it does not have non-trivial 1-dimensional representations (over the field of complex numbers C). By analogy, let us say that a finite dimensional Hopf algebra H over C is perfect if any 1-dimensional H-module is trivial. Let us say that H is biperfect if both H and H^* are perfect. Note that, H is biperfect if and only if its quantum double D(H) is biperfect. It is not easy to construct a biperfect Hopf algebra of dimension >1. The goal of this note is to describe the simplest such example we know. The biperfect Hopf algebra H we construct is based on the Mathiew group of degree 24, and it is semisimple. Therefore, it yields a negative answer to Question 7.5 from a previous paper of the first two authors (math.QA/9905168). Namely, it shows that Corollary 7.4 from this paper stating that a triangular semisimple Hopf algebra over C has a non-trivial group-like element, fails in the quasitriangular case. The counterexample is the quantum double D(H).

Affiliated with

Also associated with

No associations

Rating

Biperfect Hopf Algebras 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 Biperfect Hopf Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Biperfect Hopf Algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-23924