Rank varieties and projectivity for a class of local algebras

Journal article

We consider algebras K[X1,... , Xm]/(X i2), where K is an algebraically closed fields. To any finite dimensional module for this algebra we associate a rank variety. When char(K) = 2 we recover Carlson's rank variety. The main result states that a module is projective if and only if its rank variety vanishes. This has applications to other algebras, including tensor products of certain Brauer tree algebras and certain parabolic Hecke algebras. In addition, the result has implications for the graph structure of the stable Auslander-Reiten quiver.

Authors: Erdmann, K; Holloway, M

• Publication status: Published
• Journal: MATHEMATISCHE ZEITSCHRIFT
• Volume: 247
• Issue: 3
• Pages: 441-460
• Publication date: 2004-07-01
• DOI: 10.1007/s00209-003-0536-9
• EISSN: 1432-1823
• ISSN: 0025-5874
• Language: English