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Serre Theorem for involutory Hopf algebras
- Source :
- Cent. Eur. J. Math, Vol. 8, Issue 1 (2010), 15-21
- Publication Year :
- 2009
-
Abstract
- We call a monoidal category ${\mathcal C}$ a Serre category if for any $C$, $D \in {\mathcal C}$ such that $C\ot D$ is semisimple, $C$ and $D$ are semisimple objects in ${\mathcal C}$. Let $H$ be an involutory Hopf algebra, $M$, $N$ two $H$-(co)modules such that $M \otimes N$ 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 is invertible in $k$ are Serre categories.<br />Comment: a new version: 8 pages
- Subjects :
- Mathematics - Rings and Algebras
16W30
Subjects
Details
- Database :
- arXiv
- Journal :
- Cent. Eur. J. Math, Vol. 8, Issue 1 (2010), 15-21
- Publication Type :
- Report
- Accession number :
- edsarx.0906.2479
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.2478/s11533-009-0062-z