ON RADICALLY GRADED FINITE DIMENSIONAL QUASI-HOPF ALGEBRAS (2009)
| Citations: | 1 - 1 self |
BibTeX
@MISC{Etingof09onradically,
author = {Pavel Etingof and Shlomo Gelaki},
title = {ON RADICALLY GRADED FINITE DIMENSIONAL QUASI-HOPF ALGEBRAS},
year = {2009}
}
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Abstract
Abstract. In this paper we continue the structure theory of finite dimensional quasi-Hopf algebras started in [EG] and [G]. First, we completely describe the class of radically graded finite dimensional quasi-Hopf algebras over C, whose radical has prime codimension. As a corollary we obtain that if p> 2 is a prime then any finite tensor category over C with exactly p simple objects which are all invertible must have Frobenius-Perron dimension p N, N = 1, 2,3, 4, 5 or 7. Second, we construct new examples of finite dimensional quasi-Hopf algebras which are not twist equivalent to a Hopf algebra. For instance, to every finite dimensional simple Lie algebra g and an odd integer n, coprime to 3 if g = G2, we attach a quasi-Hopf algebra of dimension n dimg. 1.
Citations
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| 9 | A quasi-Hopf algebra freeness theorem - Schauenburg |
| 6 | Finite-dimensional quasi-Hopf algebras with radical of codimension 2 - Etingof, Gelaki |
| 5 | Finite tensor categories, submitted - Etingof, Ostrik |
| 3 | Basic quasi-Hopf algebras of dimension n3 - Gelaki |
| 2 | On fusion categories, submitted - Etingof, Nikshych, et al. |
