Transfer Maps and Virtual Projectivity

✍ Scribed by Jon F Carlson; Chuang Peng; Wayne W Wheeler

• Book ID: 102577872
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 292 KB
• Volume: 204
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1997.7486

✦ Synopsis

When G is a finite group and H is a subgroup of G, the concept of relative H-projectivity is of fundamental importance in modular representation theory. Unfortunately, in some ways the properties of relatively H-projective modules are not as closely related to other ideas of representation theory as one might hope. For example, the variety of a module bears only a weak connection to relative projectivity. The purpose of this paper is to introduce and study a related concept known as ¨irtual H-projecti¨ity that seems to be much more closely related to the theory of varieties. The study is actually carried out in the more general setting of virtual projectivity with respect to a finitely generated module W, and the main tool is a transfer map Tr that generalizes the usual transfer map Tr G with respect to W H a subgroup H.