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A categorical approach to Cuntz-Pimsner C*-algebras

Winger, Marius Lie
Master thesis
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URI
http://hdl.handle.net/11250/2352622
Date
2015
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  • Institutt for matematiske fag [2238]
Abstract
Using a $C^*$-algebra $A$, a Hilbert $A$-module $E$ and a $C^*$-correspondence $(E,\phi_E)$ we use the language of category theory to construct $\mathcalO_{(E,\phi_E)}(J)$, the Cuntz-Pimsner representation relative to an ideal $J$. We provide a complete classification, up to isomorphism, of the bijective representations admitting a gauge action as relative Cuntz-Pimsner representations relative to some ideal. By doing this we obtain a simple proof of the gauge invariant uniqueness theorem for the Cuntz-Pimsner algebra $\mathcalO_{(E,\phi_E)}$ over $(E,\phi_E)$.
Publisher
NTNU

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