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Robertson, David; Szymański, Wojciech

\(C^{\ast }\)-algebras associated to \(C^{\ast }\)-correspondences and applications to mirror quantum spheres. (English) Zbl 1272.46048

Ill. J. Math. 55, No. 3, 845-870 (2011).
Summary: The structure of the \(C^{\ast }\)-algebras corresponding to even-dimensional mirror quantum spheres is investigated. It is shown that they are isomorphic to both Cuntz-Pimsner algebras of certain \(C^{\ast }\)-correspondences and \(C^{\ast }\)-algebras of certain labelled graphs. In order to achieve this, categories of labelled graphs and \(C^{\ast }\)-correspondences are studied. A functor from labelled graphs to \(C^{\ast }\)-correspondences is constructed, such that the corresponding associated \(C^{\ast }\)-algebras are isomorphic. Furthermore, it is shown that \(C^{\ast }\)-correspondences for the mirror quantum spheres arise via a general construction of restricted direct sums.

Cited in 3 Documents

MSC:

46L08 \(C^*\)-modules
46L65 Quantizations, deformations for selfadjoint operator algebras
46L85 Noncommutative topology

Keywords:

mirror quantum spheres; Cuntz-Pimsner algebras; labelled graphs; \(C^{\ast }\)-correspondences
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\textit{D. Robertson} and \textit{W. Szymański}, Ill. J. Math. 55, No. 3, 845--870 (2011; Zbl 1272.46048)
Full Text: arXiv Euclid
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