Banach Journal of Mathematical Analysis

A Cuntz--Krieger uniqueness theorem for semigraph $C^*$-algebras

Bernhard Burgstaller

Full-text: Open access

Abstract

Higher rank semigraph algebras are introduced by mixing concepts of ultragraph algebras and higher rank graph algebras. This yields a kind of higher rank generalisation of ultragraph algebras. We prove Cuntz--Krieger uniqueness theorems for cancelling semigraph algebras and aperiodic saturated semigraph algebras.

Article information

Source
Banach J. Math. Anal., Volume 6, Number 2 (2012), 38-57.

Dates
First available in Project Euclid: 13 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1342210159

Digital Object Identifier
doi:10.15352/bjma/1342210159

Mathematical Reviews number (MathSciNet)
MR2945987

Zentralblatt MATH identifier
1260.46035

Subjects
Primary: 46L05: General theory of $C^*$-algebras
Secondary: 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]

Keywords
Higher rank semigraph algebra ultragraph labelled graph Cuntz--Krieger uniqueness aperiodic

Citation

Burgstaller, Bernhard. A Cuntz--Krieger uniqueness theorem for semigraph $C^*$-algebras. Banach J. Math. Anal. 6 (2012), no. 2, 38--57. doi:10.15352/bjma/1342210159. https://projecteuclid.org/euclid.bjma/1342210159


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