Blocks

Peter Schneider
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Peter Schneider: University of Münster, Department of Mathematics

Chapter Chapter 5 in Modular Representation Theory of Finite Groups, 2013, pp 147-173 from Springer

Abstract: Abstract This final chapter is devoted to Brauer’s theory of blocks of modular representations of G. Blocks are defined by the primitive central idempotents in the group ring of G. We introduce the concept of the defect subgroup of a block. It measures how nonsemisimple the block is as a category. We give both the module theoretic as well as the group theoretic definition and show that the two are equivalent. Using Green’s correspondences from a previous chapter we establish Brauer’s correspondences between blocks of G and blocks of subgroups of G.

Keywords: Primitive Idempotent; Group Theoretical Definition; Group Ring; Modular Representation; Defect Group (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4471-4832-6_5

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DOI: 10.1007/978-1-4471-4832-6_5

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