Bulletin of the Belgian Mathematical Society - Simon Stevin

A new look at the proof of $K$-theoretic amenability for groups acting on trees

Pierre Julg

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Abstract

We generalize the construction by Pytlik and Szwarc of uniformly bounded representations for free groups to groups acting on trees. We deduce a new version of the proof (by Alain Valette and the author, 1983) of the fact that locally compact groups acting on trees with amenable stabilizers are amenable in $K$-theory.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 22, Number 2 (2015), 263-269.

Dates
First available in Project Euclid: 28 May 2015

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1432840862

Digital Object Identifier
doi:10.36045/bbms/1432840862

Mathematical Reviews number (MathSciNet)
MR3351040

Zentralblatt MATH identifier
1327.19010

Subjects
Primary: 19K35: Kasparov theory ($KK$-theory) [See also 58J22] 19K99: None of the above, but in this section 46L80: $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22] 22D10: Unitary representations of locally compact groups 22D12: Other representations of locally compact groups

Keywords
K-theory Operator Algebras Group Representation Theory

Citation

Julg, Pierre. A new look at the proof of $K$-theoretic amenability for groups acting on trees. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 2, 263--269. doi:10.36045/bbms/1432840862. https://projecteuclid.org/euclid.bbms/1432840862


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