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Complexity and varieties for infinitely generated modules

Published online by Cambridge University Press:  24 October 2008

D. J. Benson ,
Jon F. Carlson  and
J. Rickard
D. J. Benson
Affiliation:
Department of Mathematics, University of Georgia, Athens, GA 30602, USA
Jon F. Carlson
Affiliation:
Department of Mathematics, University of Georgia, Athens, GA 30602, USA
J. Rickard
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW
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Extract

In the past fifteen years the theory of complexity and varieties of modules has become a standard tool in the modular representation theory of finite groups. Moreover the techniques have been used in the study of integral representations [8] and have been extended to the representation theories of objects such as groups of finite virtual cohomological dimension [1], infinitesimal subgroups of algebraic groups and restricted Lie algebras [14, 16]. In all cases some sort of finiteness condition on the module category has been required to make the theory work. Usually this comes in the form of stipulating that all modules under consideration be finitely generated. While the restrictions have been efficient for most applications to date, there are very good reasons for wanting to develop a theory that will accommodate infinitely generated modules. One reason might be the possibility of extending the techniques of representations to other classes of infinite groups. Another reason is that some recent work has revealed a few of the defects of the finiteness requirement. One such problem can be summarized as follows.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 118 , Issue 2 , September 1995 , pp. 223 - 243
Copyright
Copyright © Cambridge Philosophical Society 1995

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