The C*-envelope of the tensor algebra of a directed graph

Details The C*-envelope of the tensor algebra of a directed graph The C*-envelope of the tensor algebra of a directed graph

2004-11-19

arxiv.org/abs/math/0411417v2

Integral Eqnts. & Operator Thy., 56 (2006), 300-313.

Mathematics

Operator Algebras

15 pages, one reference added, one minor correction

Scientific paper

Given an arbitrary countable directed graph $G$ we prove the C*-envelope of the tensor algebra $T_+(G)$ coincides with the universal Cuntz-Krieger algebra associated with $G$. Our approach is concrete in nature and does not rely on Hilbert module machinery. We show how our results extend to the case of higher rank graphs, where an analogous result is obtained for the tensor algebra of a row-finite $k$-graph with no sources.

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