The global dimensions of crossed products and crossed coproducts.
type: Item
instance of: scholarly article
title: The global dimensions of crossed products and crossed coproducts.
zbMATH Open document ID: 1214.16027
author: Tengxia Ju
publication date: 2009-11-11T00:00:00Z
review text: If \(H\) is a semisimple cosemisimple Hopf algebra, and \(A\#_\sigma H\) is a crossed product with invertible cocycle \(\sigma\), then it is shown that \(A\#_\sigma H\) and \(A\) have the same global dimension. This equality between global dimensions is also investigated when no semisimplicity of \(H\) or \(H^*\) are assumed, and the method of twistings is used to study the dual case of crossed coproducts of coalgebras.
reviewed by: Serban Raianu
Mathematics Subject Classification ID: 16T05
Mathematics Subject Classification ID: 16E10
Mathematics Subject Classification ID: 16T15
Mathematics Subject Classification ID: 16S35
zbMATH DE Number: 5629541
zbMATH Keywords: global dimension
zbMATH Keywords: crossed products
zbMATH Keywords: crossed coproducts
zbMATH Keywords: twistings
zbMATH Keywords: cosemisimple Hopf algebras
zbMATH Keywords: coalgebras
MaRDI profile type: Publication
full work available at URL: s10114-009-6609-x
OpenAlex ID: W2406217023
cites work: On the surjectivity of some trace maps
cites work: Induction from elementary abelian subgroups
cites work: Global dimensions of crossed products
cites work: On Crossed Products of Hopf Algebras
cites work: GLOBAL DIMENSION FOR HOPF ACTIONS
cites work: Homological dimension of skew group rings and crossed products
cites work: A NOTE ON THE GLOBAL DIMENSION OF SMASH PRODUCTS
cites work: Homological dimension of coalgebras and crossed coproducts
cites work: Q5590089
cites work: Crossed Products and Inner Actions of Hopf Algebras
cites work: Q3717232
cites work: Crossed products and Galois extensions of Hopf algebras
cites work: Q4703398
cites work: Semisimple Cosemisimple Hopf Algebras
cites work: Finite dimensional cosemisimple Hopf algebras in characteristic 0 are semisimple
cites work: On Kaplansky's fifth conjecture
cites work: Hereditary coalgebras
cites work: Crossed coproducts and cleft coextensions
cites work: Genaralization fo cleft comodule algabras
cites work: Twisted hopf comodule algebras
cites work: Twisted hopf module coalgebras
DOI: 10.1007/S10114-009-6609-X
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5629541