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Journal of the London Mathematical Society 1997 56(1):149-170; doi:10.1112/S0024610797005309
© 1997 by London Mathematical Society
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© The London Mathematical Society

Idempotent Modules in the Stable Category

Jeremy Rickard

School of Mathematics, University of Bristol University Walk, Bristol BS8 1TW. E-mail address: J.Rickard{at}bristol.ac.uk

Received 10 January 1994. Revision received 10 June 1995.

Let G be a finite group and k be an algebraically closed field of prime characteristic. Corresponding to each closed homogeneous subvariety W of the maximal ideal spectrum of H*(G, k) we construct (usually infinite-dimensional) kG-modules E(W) and F(W) which are idempotent in the sense that E(W) and F(W) are isomorphic (up to projective summands) to E(W) {otimes} E(W) and F(W) {otimes} F(W) respectively. We study the properties of these modules, and as an application we use them to describe natural direct sum decompositions of modules in quotient categories.


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