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K-THEORY FOR THE C*-ALGEBRAS OF THE SOLVABLE BAUMSLAG–SOLITAR GROUPS

Published online by Cambridge University Press:  18 October 2017

SANAZ POOYA
Affiliation:
Institut de Mathéematiques, Université de Neuchâtel Unimail, Rue Emile Argand 11 CH-2000 Neuchatel, Switzerland e-mail: sanaz.pooya@unine.ch, alain.valette@unine.ch
ALAIN VALETTE
Affiliation:
Institut de Mathéematiques, Université de Neuchâtel Unimail, Rue Emile Argand 11 CH-2000 Neuchatel, Switzerland e-mail: sanaz.pooya@unine.ch, alain.valette@unine.ch

Abstract

We provide a new computation of the K-theory of the group C*-algebra of the solvable Baumslag–Solitar group BS(1, n) (n ≠ 1); our computation is based on the Pimsner–Voiculescu 6-terms exact sequence, by viewing BS(1, n) as a semi-direct product ℤ[1/n] ⋊ ℤ. We deduce from it a new proof of the Baum–Connes conjecture with trivial coefficients for BS(1, n).

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

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K-THEORY FOR THE C*-ALGEBRAS OF THE SOLVABLE BAUMSLAG–SOLITAR GROUPS
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