Corners of Cuntz-Krieger algebras
نویسندگان
چکیده
منابع مشابه
Cuntz-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 کاملGraphs, 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 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.
متن کاملRepresentations of the Cuntz - Krieger algebras . I — General theory —
Representation theory of the Cuntz algebras is studied by [4, 6, 7, 8, 9, 16, 17]. It is remarkable that representations of the Cuntz algebras in some class satisfy the uniqueness of irreducible decomposition. Furthermore these representations are related to quantum filed theory([1, 2, 3]), dynamical systems([11, 13, 14, 15]) and fractals([12]), and their branching laws are computed by automata...
متن کاملTopological Entropy for the Canonical Endomorphism of Cuntz-krieger Algebras
and φA is the endomorphism induced on C(XA) by the one-sided subshift of finite type σA (see [6]) defined by (σAx)k = xk+1, x = (xk)k∈N ∈ XA. Therefore φA can be regarded as a non-commutative generalization of the one-sided subshift of finite type associated with the matrix A and the computation of its dynamical entropies is of some interest (see [4, Page 691]). When A(i, i) = 1, i ∈ Σ, one get...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2015
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-2015-06283-7