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The K-theory of the conjugation action
Comptes Rendus. Mathématique, Tome 359 (2021) no. 7, pp. 795-796.

In 1999, Brylinski and Zhang computed the complex equivariant K-theory of the conjugation self-action of a compact, connected Lie group with torsion-free fundamental group. In this note we show it is possible to do so in under a page.

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DOI : https://doi.org/10.5802/crmath.235
Jeffrey D. Carlson 1

1. Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, UK
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Jeffrey D. Carlson. The K-theory of the conjugation action. Comptes Rendus. Mathématique, Tome 359 (2021) no. 7, pp. 795-796. doi : 10.5802/crmath.235. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.235/

[1] Michael F. Atiyah On the K-theory of compact Lie groups, Topology, Volume 4 (1965) no. 1, pp. 95-99 | Article | MR 178092 | Zbl 0136.21001

[2] Jean-Luc Brylinski; Bin Zhang Equivariant K-theory of compact connected Lie groups, K-Theory, Volume 20 (2000) no. 1, pp. 23-36 | Article | MR 1798430 | Zbl 0971.19003

[3] Chi-Kwong Fok The Real K-theory of compact Lie groups, SIGMA, Symmetry Integrability Geom. Methods Appl., Volume 10 (2014), 022, 26 pages | Article | MR 3210613 | Zbl 1291.19007

[4] Luke Hodgkin On the K-theory of Lie groups, Topology, Volume 6 (1967) no. 1, pp. 1-36 | Article | MR 214099

[5] Luke Hodgkin The equivariant Künneth theorem in K-theory, Topics in K-theory (Lecture Notes in Mathematics), Volume 496, Springer, 1975, pp. 1-101 | Article | MR 478156

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