C*-algebras associated to C*-correspondences and applications to mirror quantum spheres

David Robertson; Wojciech Szymanski

doi:10.1215/ijm/1369841788

C-algebras associated to C-correspondences and applications to mirror quantum spheres

David Robertson
, Wojciech Szymanski

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

The structure of the C^∗-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^∗-correspondences and C^∗-algebras of certain labelled graphs. In order to achieve this, categories of labelled graphs and C^∗-correspondences are studied. A functor from labelled graphs to C^∗-correspondences is constructed, such that the corresponding associated C^∗-algebras are isomorphic. Furthermore, it is shown that C^∗-correspondences for the mirror quantum spheres arise via a general construction of restricted direct sum.

Original language	English
Pages (from-to)	845-870
Journal	Illinois Journal of Mathematics
Volume	55
Issue number	3
DOIs	https://doi.org/10.1215/ijm/1369841788
Publication status	Published - 2011

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title = "C*-algebras associated to C*-correspondences and applications to mirror quantum spheres",

abstract = "The structure of the C∗-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∗-correspondences and C∗-algebras of certain labelled graphs. In order to achieve this, categories of labelled graphs and C∗-correspondences are studied. A functor from labelled graphs to C∗-correspondences is constructed, such that the corresponding associated C∗-algebras are isomorphic. Furthermore, it is shown that C∗-correspondences for the mirror quantum spheres arise via a general construction of restricted direct sum.",

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AU - Robertson, David

AU - Szymanski, Wojciech

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N2 - The structure of the C∗-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∗-correspondences and C∗-algebras of certain labelled graphs. In order to achieve this, categories of labelled graphs and C∗-correspondences are studied. A functor from labelled graphs to C∗-correspondences is constructed, such that the corresponding associated C∗-algebras are isomorphic. Furthermore, it is shown that C∗-correspondences for the mirror quantum spheres arise via a general construction of restricted direct sum.

AB - The structure of the C∗-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∗-correspondences and C∗-algebras of certain labelled graphs. In order to achieve this, categories of labelled graphs and C∗-correspondences are studied. A functor from labelled graphs to C∗-correspondences is constructed, such that the corresponding associated C∗-algebras are isomorphic. Furthermore, it is shown that C∗-correspondences for the mirror quantum spheres arise via a general construction of restricted direct sum.

U2 - 10.1215/ijm/1369841788

DO - 10.1215/ijm/1369841788

M3 - Article

SN - 0019-2082

VL - 55

SP - 845

EP - 870

JO - Illinois Journal of Mathematics

JF - Illinois Journal of Mathematics

IS - 3