The Cartan–Brauer Triangle

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

Chapter Chapter 2 in Modular Representation Theory of Finite Groups, 2013, pp 43-86 from Springer

Abstract: Abstract In this chapter we use certain local integral domains with field of fractions K of characteristic zero and with algebraically closed residue class field k of positive characteristic p to relate the representation theories of a finite group G over K and over k. This is done on the level of Grothendieck groups and leads to the Cartan homomorphism and the decomposition homomorphism of G, which are two basic invariants of modular representation theory. Technically we have to introduce the Burnside ring, have to develop Clifford theory, and have to prove several major induction theorems.

Keywords: Burnside Ring; Decomposition Homomorphism; Local Integral Domain; Grothendieck Group; Characteristic Zero (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-1-4471-4832-6_2

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