Vertex and source determine the block variety of an indecomposable module

David John Benson, Markus Linckelmann

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


The block variety V-G.b(M) of a finitely generated indecomposable module M over the block algebra of a p-block b of a finite group G, introduced in (J. Algebra 215 (1999) 460), can be computed in terms of a vertex and a source of M. We use this to show that VG,b(M) is connected, and that every closed homogeneous subvariety of the affine variety VG.b defined by block cohomology H*(G, b) (cf. Al.-ebras Rep. Theory 2 (1999) 107) is the variety of a module over the block algebra. This is analogous to the corresponding statements on Carlson's cohomology varieties in (lnvent. Math. 77 (1984) 291). © 2004 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)11-17
Number of pages7
JournalJournal of Pure and Applied Algebra
Issue number1-3
Early online date21 Nov 2004
Publication statusPublished - 1 May 2005


  • source algebras


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