Graded coalgebras and Morita-Takeuchi contexts
type: Item
instance of: scholarly article
title: Graded coalgebras and Morita-Takeuchi contexts
zbMATH Open document ID: 0859.16032
author: Constantin Năstăsescu
author: Sorin Dascalescu
author: Serban Raianu
author: Fred Van Oystaeyen
published in: Tsukuba Journal of Mathematics
publication date: 1996-08-29T00:00:00Z
review text: Let \(G\) be a group and \(k\) a field. The present paper deals with \(G\)-graded coalgebras \(C=\bigoplus_{g\in G}C_g\), that is, with right \(kG\)-comodule coalgebras, and with graded \(C\)-comodules, that is, comodules over the smash product \(C\rtimes kG\). The authors continue the investigation started by \textit{C. Năstăsescu} and \textit{B. Torrecillas} [Tsukuba J. Math. 17, No. 2, 461-479 (1993; Zbl 0819.16036)]. Their main result is as follows. The coalgebras \(C_1\) and \(C\rtimes kG\) are connected by a Morita-Takeuchi context in which one of the structure maps is injective. Some applications of this result are also given. It is proved that \(C\) is strongly graded iff the other structure map is injective. Finally two duality theorems are obtained, these being analogues of the Cohen-Montgomery duality theorems for groups acting and coacting on algebras.
reviewed by: Andrei Marcus
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16S40
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 16W50
zbMATH DE Number: 895946
zbMATH Keywords: graded coalgebras
zbMATH Keywords: right comodule coalgebras
zbMATH Keywords: graded comodules
zbMATH Keywords: smash products
zbMATH Keywords: Morita-Takeuchi contexts
zbMATH Keywords: duality theorems
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496162878
OpenAlex ID: W1703780898
DOI: 10.21099/TKBJM/1496162878
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description: scientific article; zbMATH DE number 895946