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On the K-theory of boundary C*-algebras of Ã2 groups

Published online by Cambridge University Press:  21 June 2011

Oliver King  and
Guyan Robertson
Oliver King
Affiliation:
School of Mathematics and Statistics, University of Newcastle, NE1 7RU, Englando.h.king@ncl.ac.uk
Guyan Robertson
Affiliation:
School of Mathematics and Statistics, University of Newcastle, NE1 7RU, Englanda.g.robertson@ncl.ac.uk
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Abstract

Let Γ be an Ã2 subgroup of PGL3(), where is a local field with residue field of order q. The module of coinvariants C(,ℤ)Γ is shown to be finite, where is the projective plane over . If the group Γ is of Tits type and if q ≢ 1 (mod 3) then the exact value of the order of the class [1]K0 in the K-theory of the (full) crossed product C*-algebra C(Ω) ⋊ Γ is determined, where Ω is the Furstenberg boundary of PGL3(). For groups of Tits type, this verifies a conjecture of G. Robertson and T. Steger.

Keywords

affine buildingboundaryoperator algebra
Type
Research Article
Information
Journal of K-Theory , Volume 9 , Issue 3 , June 2012 , pp. 521 - 536
Copyright
Copyright © ISOPP 2011

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