The theory of Toeplitz algebras of rightangled Artin groups
Author:
Nikolay A. Ivanov
Journal:
Trans. Amer. Math. Soc. 362 (2010), 60036027
MSC (2010):
Primary 19K99, 46L80; Secondary 46L35
Published electronically:
May 19, 2010
MathSciNet review:
2661506
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Abstract: Toeplitz algebras of rightangled Artin groups were studied by Crisp and Laca. They are a special case of the Toeplitz algebras associated with quasilattice ordered groups introduced by Nica. Crisp and Laca proved that the socalled ``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 PimsnerVoiculescu exact sequence to find their theory. Finally we use the KirchbergPhillips 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:
http://dx.doi.org/10.1090/S000299472010051621
PII:
S 00029947(2010)051621
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.
