Equivariant K-theory of finite dimensional real vector spaces

2009/03/05 by Siegfried Echterhoff, Echterhoff, Siegfried, Oliver Pfante +1 · 1 citation
Mathematics · #19K99 #19L64 #46L80 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.0903.1035

openalex publication_date 2009/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a general formula for the equivariant complex K-theory K_G^*(V) of a finite dimensional real linear space V equipped with a linear action of a compact group G in terms of the representation theory of a certain double cover of G. Using this general formula, we give explicit computations in various interesting special cases. In particular, as an application we obtain explicit formulas for the K-theory of C_r^*(GL(n,\RR)), the reduced group C*-algebra of GL(n,\RR).

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