Quantum lens spaces and graph algebras
نویسندگان
چکیده
منابع مشابه
Quantum Lens Spaces and Graph Algebras
We construct the C∗-algebra C(Lq(p;m1, . . . ,mn)) of continuous functions on the quantum lens space as the fixed point algebra for a suitable action of Zp on the algebra C(S2n−1 q ), corresponding to the quantum odd dimensional sphere. We show that C(Lq(p;m1, . . . ,mn)) is isomorphic to the graph algebra C∗ ( L (p;m1,...,mn) 2n−1 ) . This allows us to determine the ideal structure and, at lea...
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We study certain principal actions on noncommutative C-algebras. Our main examples are the Zpand T-actions on the odd-dimensional quantum spheres, yielding as fixed-point algebras quantum lens spaces and quantum complex projective spaces, respectively. The key tool in our analysis is the relation of the ambient C-algebras with the Cuntz-Krieger algebras of directed graphs. A general result abou...
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Let X denote an arbitrary second-countable, compact, zero-dimensional space. Our main result says that A' is a graph space, i.e., homeomorphic to the space of all complete subgraphs of a suitable graph. We first characterize graph spaces in terms of the Boolean algebras of their clopen subsets. Then it is proved that each countable Boolean algebra has the corresponding property. As a corollary ...
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Let l be a length function on a group G, and let Ml denote the operator of pointwise multiplication by l on l(G). Following Connes, Ml can be used as a “Dirac” operator for C ∗ r (G). It defines a Lipschitz seminorm on C∗ r (G), which defines a metric on the state space of C∗ r (G). We show that if G is a hyperbolic group and if l is a word-length function on G, then the topology from this metr...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2003
ISSN: 0030-8730
DOI: 10.2140/pjm.2003.211.249