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

Author(s): Takeshi Katsura
Journal: Trans. Amer. Math. Soc. 356 (2004), 4287-4322.
MSC (2000): Primary 46L05; Secondary 46L55, 37B99
Posted: May 28, 2004
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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: 10.1090/S0002-9947-04-03636-0
PII: S 0002-9947(04)03636-0
Received by editor(s): October 1, 2002
Posted: May 28, 2004
Copyright of article: Copyright 2004, American Mathematical Society

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