The -theory of Toeplitz -algebras of right-angled Artin groups

Author:
Nikolay A. Ivanov

Journal:
Trans. Amer. Math. Soc. **362** (2010), 6003-6027

MSC (2010):
Primary 19K99, 46L80; Secondary 46L35

DOI:
https://doi.org/10.1090/S0002-9947-2010-05162-1

Published electronically:
May 19, 2010

MathSciNet review:
2661506

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Abstract: Toeplitz -algebras of right-angled Artin groups were studied by Crisp and Laca. They are a special case of the Toeplitz -algebras associated with quasi-lattice ordered groups introduced by Nica. Crisp and Laca proved that the so-called ``boundary quotients'' of are simple and purely infinite. For a certain class of finite graphs we show that can be represented as a full corner of a crossed product of an appropriate -subalgebra of built by using , where is a subgraph of with one less vertex, by the group . Using induction on the number of the vertices of we show that are nuclear and moreover belong to the small bootstrap class. We also use the Pimsner-Voiculescu exact sequence to find their -theory. Finally we use the Kirchberg-Phillips classification theorem to show that those -algebras are isomorphic to tensor products of with .

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Additional Information

**Nikolay A. Ivanov**

Affiliation:
Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada K7L 3N6

Address at time of publication:
18 Momina Krepost Str., apt. 3, Veliko Turnovo, 5000 Bulgaria

Email:
nikolay.antonov.ivanov@gmail.com

DOI:
https://doi.org/10.1090/S0002-9947-2010-05162-1

Received by editor(s):
November 9, 2007

Received by editor(s) in revised form:
March 3, 2009

Published electronically:
May 19, 2010

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.