✦ LIBER ✦

A Maschke Type Theorem for Doi–Hopf Modules and Applications

✍ Scribed by S. Caenepeel; G. Militaru; Zhu Shenglin

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 239 KB
Volume: 187
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.6794

No coin nor oath required. For personal study only.

✦ Synopsis

We prove a Maschke type theorem for Doi᎐Hopf modules. A sufficient condition in order to have a Maschke type property is that there exists a normalized integral map for the Doi᎐Hopf datum in question. The results are applied to graded modules and to Yetter᎐Drinfel'd modules. As another application, a characterization of cosemisimple coalgebras over a field is given.