Hilbert C*-bimodules and continuous Cuntz-Krieger algebras
نویسندگان
چکیده
منابع مشابه
Graphs, groupoids and Cuntz-Krieger algebras
We associate to each locally finite directed graph G two locally compact groupoids G and G(?). The unit space of G is the space of one–sided infinite paths in G, and G(?) is the reduction of G to the space of paths emanating from a distinguished vertex ?. We show that under certain conditions their C∗–algebras are Morita equivalent; the groupoid C∗–algebra C∗(G) is the Cuntz–Krieger algebra of ...
متن کاملCuntz-Krieger algebras of directed graphs
We associate to each row-finite directed graph E a universal Cuntz-Krieger C∗-algebra C∗(E), and study how the distribution of loops in E affects the structure of C∗(E). We prove that C∗(E) is AF if and only if E has no loops. We describe an exit condition (L) on loops in E which allows us to prove an analogue of the Cuntz-Krieger uniqueness theorem and give a characterisation of when C∗(E) is ...
متن کاملCuntz-krieger Algebras and a Generalization of Catalan Numbers
We first observe that the relations of the canonical generating isometries of the Cuntz algebra ON are naturally related to the N-colored Catalan numbers. For a directed graph G, we generalize the Catalan numbers by using the canonical generating partial isometries of the Cuntz-Krieger algebra O AG for the transition matrix A of G. The generalized Catalan numbers cGn , n = 0, 1, 2, . . . enumer...
متن کاملCuntz-Krieger-Pimsner Algebras Associated with Amalgamated Free Product Groups
We give a construction of a nuclear C∗-algebra associated with an amalgamated free product of groups, generalizing Spielberg’s construction of a certain Cuntz-Krieger algebra associated with a finitely generated free product of cyclic groups. Our nuclear C∗-algebras can be identified with certain Cuntz-Krieger-Pimsner algebras. We will also show that our algebras can be obtained by the crossed ...
متن کاملThe Classification of Two-component Cuntz-krieger Algebras
Cuntz-Krieger algebras with exactly one non-trivial closed ideal are classiied up to stable isomorphism by the Cuntz invariant. The proof relies on RRrdam's classiication of simple Cuntz-Krieger algebras up to stable isomorphism and the author's classiication of two-component reducible topological Markov chains up to ow equivalence.
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 2002
ISSN: 0025-5645
DOI: 10.2969/jmsj/1191593954