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A class of $C^*$-algebras generalizing both graph algebras and homeomorphism $C^*$-algebras I, fundamental results


Author: Takeshi Katsura
Journal: Trans. Amer. Math. Soc. 356 (2004), 4287-4322
MSC (2000): Primary 46L05; Secondary 46L55, 37B99
DOI: https://doi.org/10.1090/S0002-9947-04-03636-0
Published electronically: May 28, 2004
MathSciNet review: 2067120
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Abstract: We introduce a new class of $C^*$-algebras, which is a generalization of both graph algebras and homeomorphism $C^*$-algebras. This class is very large and also very tractable. We prove the so-called gauge-invariant uniqueness theorem and the Cuntz-Krieger uniqueness theorem, and compute the $K$-groups of our algebras.


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Additional Information

Takeshi Katsura
Affiliation: Department of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153-8914, Japan
Address at time of publication: Department of Mathematics, Hokkaido University, Sapporo, Hokkaido 060-0810, Japan
Email: katsura@math.sci.hokudai.ac.jp

DOI: https://doi.org/10.1090/S0002-9947-04-03636-0
Received by editor(s): October 1, 2002
Published electronically: May 28, 2004
Article copyright: © Copyright 2004 American Mathematical Society

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