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A class of \boldmath{$C^*$}-algebras generalizing both graph algebras and homeomorphism \boldmath{$C^*$}-algebras I, fundamental results
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.