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The co-universal C*-algebra of a row-finite graph

Journal Article


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Abstract


  • Let $E$ be a row-finite directed graph. We prove that there exists a $C^*$-algebra $\Cr{E}$ with the following co-universal property: given any $C^*$-algebra $B$ generated by a Toeplitz-Cuntz-Krieger $E$-family in which all the vertex projections are nonzero, there is a canonical homomorphism from $B$ onto $\Cr{E}$. We also identify when a homomorphism from $B$ to $\Cr{E}$ obtained from the co-universal property is injective. When every loop in $E$ has an entrance, $\Cr{E}$ coincides with the graph $C^*$-algebra $C^*(E)$, but in general, $\Cr{E}$ is a quotient of $C^*(E)$. We investigate the

    properties of $\Cr{E}$ with emphasis on the utility of co-universality as the defining property of the algebra.

Publication Date


  • 2010

Citation


  • Sims, A. (2010). The co-universal C*-algebra of a row-finite graph. New York Journal of Mathematics, 16 507-524.

Scopus Eid


  • 2-s2.0-84055191529

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1852&context=infopapers

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/836

Number Of Pages


  • 17

Start Page


  • 507

End Page


  • 524

Volume


  • 16

Place Of Publication


  • http://nyjm.albany.edu:8000/Papers.html

Abstract


  • Let $E$ be a row-finite directed graph. We prove that there exists a $C^*$-algebra $\Cr{E}$ with the following co-universal property: given any $C^*$-algebra $B$ generated by a Toeplitz-Cuntz-Krieger $E$-family in which all the vertex projections are nonzero, there is a canonical homomorphism from $B$ onto $\Cr{E}$. We also identify when a homomorphism from $B$ to $\Cr{E}$ obtained from the co-universal property is injective. When every loop in $E$ has an entrance, $\Cr{E}$ coincides with the graph $C^*$-algebra $C^*(E)$, but in general, $\Cr{E}$ is a quotient of $C^*(E)$. We investigate the

    properties of $\Cr{E}$ with emphasis on the utility of co-universality as the defining property of the algebra.

Publication Date


  • 2010

Citation


  • Sims, A. (2010). The co-universal C*-algebra of a row-finite graph. New York Journal of Mathematics, 16 507-524.

Scopus Eid


  • 2-s2.0-84055191529

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1852&context=infopapers

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/836

Number Of Pages


  • 17

Start Page


  • 507

End Page


  • 524

Volume


  • 16

Place Of Publication


  • http://nyjm.albany.edu:8000/Papers.html