Green’s Theory of Indecomposable Modules

Peter Schneider
Additional contact information
Peter Schneider: University of Münster, Department of Mathematics

Chapter Chapter 4 in Modular Representation Theory of Finite Groups, 2013, pp 97-146 from Springer

Abstract: Abstract This chapter explains one of the cornerstones of the module theoretic approach to modular representation theory. By using the notion of a relatively projective module one obtains a means to measure how far away a module over a group ring of G is from being projective. This leads to the concepts of vertices and sources of such modules. The theory is used to establish Green’s correspondences between indecomposable modules of G and of specific subgroups of G. We prove Green’s theorem that induction from a normal subgroup whose index in G is a power of p preserves indecomposability of modular representations. We also make explicit all concepts and results developed so far for the group $\mathit{SL}_{2}(\mathbb{F}_{p})$ .

Keywords: Module-theoretic Approach; Relatively Projective; Greater Correspondence; Krull Remak Schmidt Theorem; Isomorphism Classes (search for similar items in EconPapers)
Date: 2013
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4471-4832-6_4

Ordering information: This item can be ordered from
http://www.springer.com/9781447148326

DOI: 10.1007/978-1-4471-4832-6_4

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().