Partial crossed product description of the -algebras associated with integral domains

Authors:
Giuliano Boava and Ruy Exel

Journal:
Proc. Amer. Math. Soc. **141** (2013), 2439-2451

MSC (2010):
Primary 46L05, 46L55

DOI:
https://doi.org/10.1090/S0002-9939-2013-11724-7

Published electronically:
April 3, 2013

MathSciNet review:
3043025

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Abstract: Recently, Cuntz and Li introduced the -algebra associated to an integral domain with finite quotients. In this paper, we show that is a partial group algebra of the group with suitable relations, where is the field of fractions of . We identify the spectrum of these relations and we show that it is homeomorphic to the profinite completion of . By using partial crossed product theory, we reconstruct some results proved by Cuntz and Li. Among them, we prove that is simple by showing that the action is topologically free and minimal.

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Additional Information

**Giuliano Boava**

Affiliation:
Instituto Nacional de Matemática Pura e Aplicada, 22460-320, Rio de Janeiro/RJ, Brazil

Address at time of publication:
Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-900, Florianópolis/SC, Brazil

Email:
gboava@gmail.com

**Ruy Exel**

Affiliation:
Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-900, Florianópolis/SC, Brazil

Email:
r@exel.com.br

DOI:
https://doi.org/10.1090/S0002-9939-2013-11724-7

Received by editor(s):
May 23, 2011

Received by editor(s) in revised form:
October 22, 2011

Published electronically:
April 3, 2013

Additional Notes:
The first author’s research was supported by CNPq, Brazil

The second author’s research was partially supported by CNPq, Brazil

Communicated by:
Marius Junge

Article copyright:
© Copyright 2013
American Mathematical Society

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