Construction and pure infiniteness of $C^*$-algebras associated with lambda-graph systems

Authors

  • Kengo Matsumoto

DOI:

https://doi.org/10.7146/math.scand.a-14964

Abstract

A $\lambda$-graph system is a labeled Bratteli diagram with shift transformation. It is a generalization of finite labeled graphs and presents a subshift. In [16] the author has introduced a $C^*$-algebra $\mathcal{O}_{\mathfrak{L}}$ associated with a $\lambda$-graph system $\mathfrak{L}$ by using groupoid method as a generalization of the Cuntz-Krieger algebras. In this paper, we concretely construct the $C^*$-algebra $\mathcal{O}_{\mathfrak{L}}$ by using both creation operators and projections on a sub Fock Hilbert space associated with $\mathfrak{L}$. We also introduce a new irreducible condition on $\mathfrak{L}$ under which the $C^*$-algebra $\mathcal{O}_{\mathfrak{L}}$ becomes simple and purely infinite.

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Published

2005-09-01

How to Cite

Matsumoto, K. (2005). Construction and pure infiniteness of $C^*$-algebras associated with lambda-graph systems. MATHEMATICA SCANDINAVICA, 97(1), 73–88. https://doi.org/10.7146/math.scand.a-14964

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Section

Articles