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Projective modules, augmentation and idempotents in group algebras

✍ Scribed by Ioannis Emmanouil

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
106 KB
Volume
158
Category
Article
ISSN
0022-4049

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✦ Synopsis

We consider a condition on a group G, that was studied by Strebel and independently by Strojnowski, which implies that the complex group algebra of G has no non-trivial idempotents. We elaborate on that technique and slightly relax the Strebel-Strojnowski condition. This enables us to prove in a relatively simple way certain closure properties for the resulting class of groups.

πŸ“œ SIMILAR VOLUMES

Quadratic Geometries, Projective Modules
Quadratic Geometries, Projective Modules, and Idempotents
✍ R. Gow; W. Willems πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 463 KB

Let \(G\) be a finite group and let \(k\) be a field. We say that a \(k G\)-module \(V\) has a quadratic geometry or is of quadratic type if there exists a non-degenerate (equivalently non-singular) \(G\)-invariant quadratic form on \(V\). If \(V\) is irreducible or projective indecomposable and \(k