Coactions on spaces of morphisms.
type: Item
instance of: scholarly article
title: Coactions on spaces of morphisms.
zbMATH Open document ID: 1184.16035
published in: Algebras and Representation Theory
publication date: 2009-09-01T00:00:00Z
review text: Let \(H\) be a Hopf algebra over the field \(k\). The authors show that an involutory Hopf algebra with non-zero integral verifying that there exists an injective indecomposable right comodule with dimension not divisible by the characteristic of \(k\) is cosemisimple. In particular, in characteristic zero, an involutory Hopf algebra with non-zero integral is always cosemisimple. This is a new proof of a result by \textit{J. B. Sullivan} [J. Algebra 19, 426-440 (1971; Zbl 0239.16006)]. Moreover, the following extension of a result of \textit{R. G. Larson} [J. Algebra 17, 352-368 (1971; Zbl 0217.33801)] is obtained: for a cosemisimple Hopf algebra, the characteristic of \(k\) does not divide the dimension of any absolutely irreducible right comodule.
Mathematics Subject Classification ID: 16T15
Mathematics Subject Classification ID: 16T05
zbMATH DE Number: 5600723
zbMATH Keywords: involutory Hopf algebras
zbMATH Keywords: integrals
zbMATH Keywords: simple comodules
zbMATH Keywords: injective comodules
zbMATH Keywords: cosemisimple Hopf algebras
author: Sorin Dascalescu
author: Constantin Năstăsescu
reviewed by: Blas Torrecillas
MaRDI profile type: Publication
full work available at URL: s10468-009-9154-5
OpenAlex ID: W1999688417
cites work: On the Cohomology of Relative Hopf Modules
cites work: Symmetric coalgebras.
cites work: On Hopf Algebras with Nonzero Integral
cites work: INVOLUTORY HOPF ALGEBRAS WITH NON-ZERO INTEGRALS
cites work: Homological coalgebra
cites work: Characters of Hopf algebras
cites work: Semiperfect coalgebras
cites work: Representations of finite-dimensional Hopf algebras
cites work: The wedderburn-malcev theorem for comodule algebras
cites work: The uniqueness of integrals for Hopf algebras and some existence theorems of integrals for commutative Hopf algebra
cites work: Smash products and comodules of linear maps
DOI: 10.1007/S10468-009-9154-5
description: scientific article; zbMATH DE number 5600723