Biperfect Hopf Algebras
| dc.creator | Etingof, Pavel | |
| dc.creator | Gelaki, Shlomo | |
| dc.creator | Guralnick, Robert | |
| dc.creator | Saxl, Jan | |
| dc.date | 1999-12-08 | |
| dc.date.accessioned | 2026-07-07T05:32:12Z | |
| dc.date.available | 2026-07-07T05:32:12Z | |
| dc.description | 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). | |
| dc.description | 5 pages, latex | |
| dc.identifier | https://arxiv.org/abs/math/9912068 | |
| dc.identifier | http://arxiv.org/abs/math/9912068 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79572 | |
| dc.subject | Quantum Algebra | |
| dc.title | Biperfect Hopf Algebras | |
| dc.type | text |