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

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  18 October 2017

SANAZ POOYA  and
ALAIN VALETTE
SANAZ POOYA
Affiliation:
Institut de Mathéematiques, Université de Neuchâtel Unimail, Rue Emile Argand 11 CH-2000 Neuchatel, Switzerland e-mail: [email protected], [email protected]
ALAIN VALETTE
Affiliation:
Institut de Mathéematiques, Université de Neuchâtel Unimail, Rue Emile Argand 11 CH-2000 Neuchatel, Switzerland e-mail: [email protected], [email protected]
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Abstract

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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).

MSC classification

Primary: 46L80: $K$-theory and operator algebras (including cyclic theory)
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 2 , May 2018 , pp. 481 - 486
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

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