Equivariant K-Theory of Simply Connected Lie Groups

1997/10/30 by Jean-Luc Brylinski, Bin Zhang, Brylinski, Jean-Luc +1 · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #dg-ga #math.DG #math.KT

paper · pdf · doi:10.48550/arxiv.dg-ga/9710035

16pages, 1 figure

openalex publication_date 1997/10/30 · arxiv created 1999/03/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the equivariant K-theory K_G^*(G) for a simply connected Lie group G (acting on itself by conjugation). We prove that K_G^*(G) is isomorphic to the algebra of Grothendieck differentials on the representation ring. We also study a special example of a non-simply connected Lie group G, namely PSU(3), and compute the corresponding equivariant K-theory.

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• Gerbes on complex reductive Lie groups

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