Serre Theorem for involutory Hopf algebras

• Autorzy: Gigel Militaru
• Języki publikacji: EN

Abstrakty

EN

We call a monoidal category C a Serre category if for any C, D ∈ C such that C ⊗ D is semisimple, C and D are semisimple objects in C. Let H be an involutory Hopf algebra, M, N two H-(co)modules such that M ⊗ N is (co)semisimple as a H-(co)module. If N (resp. M) is a finitely generated projective k-module with invertible Hattory-Stallings rank in k then M (resp. N) is (co)semisimple as a H-(co)module. In particular, the full subcategory of all finite dimensional modules, comodules or Yetter-Drinfel’d modules over H the dimension of which are invertible in k are Serre categories.

Słowa kluczowe

EN

Hopf algebras; Semisimple modules; Chevalley property

Kategorie tematyczne

• 16S40: Smash products of general Hopf actions

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 1
• Strony: 15-21

Daty

wydano

2010-02-01

online

2010-02-02

Twórcy

autor

Gigel Militaru

• University of Bucharest

Bibliografia

• [1] Andruskiewitsch N., Etingof P., Gelaki S., Triangular Hopf algebras with the Chevalley property, Michigan Math. J., 2001, 49, 277–298 http://dx.doi.org/10.1307/mmj/1008719774
• [2] Chevalley C., Theorie des Groupes de Lie, Vol. III, Hermann, Paris, 1954
• [3] Lambe L.A., Radford D., Algebraic aspects of the quantum Yang-Baxter equation, J. Algebra, 1992, 154, 222–288
• [4] Serre J.-P., Sur la semi-simplicitï’·e des produits tensoriels de reprï’·esentations de groupes, Invent. Math., 1994, 116, 513–530 http://dx.doi.org/10.1007/BF01231571
• [5] Serre J.-P., Semisimplicity and tensor products of group representations: converse theorems, J. Algebra, 1997, 194, 496–520 http://dx.doi.org/10.1006/jabr.1996.6929
• [6] Serre J.-P., Moursund Lectures 1998, Notes by Duckworth W.E., preprint availabe at http://math.uoregon.edu/resources/serre/

Identyfikatory

DOI

10.2478/s11533-009-0062-z