Purely infinite crossed products by endomorphisms

We study the crossed product C⁎-algebra associated to injective endomorphisms, which turns out to be equivalent to study the crossed product by the dilated automorphism. We prove that the dilation of the Bernoulli p-shift endomorphism is topologically free. As a consequence, we have a way to twist a...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2014-04, Vol.412 (1), p.466-477
Main Authors: Ortega, Eduard, Pardo, Enrique
Format: Article
Language:English
Subjects:
Crossed product
Dilation
Purely infinite
Rokhlin property
Shift endomorphism
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Summary:We study the crossed product C⁎-algebra associated to injective endomorphisms, which turns out to be equivalent to study the crossed product by the dilated automorphism. We prove that the dilation of the Bernoulli p-shift endomorphism is topologically free. As a consequence, we have a way to twist any endomorphism of a D-absorbing C⁎-algebra into one whose dilated automorphism is essentially free and have the same K-theory map than the original one. This allows us to construct purely infinite crossed products C⁎-algebras with diverse ideal structures.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2013.10.078