Journal of Operator Theory

Volume 42, Issue 2, Fall 1999 pp. 351-370.

A simple $C^*$-algebra arising from a certain subshift

Authors: Kengo Matsumoto
Author institution: Department of Mathematics, Joetsu University of Education, Joetsu 943--8512, Japan

Summary: We present an example of a subshift whose associated $C^*$-alge\-bra is simple, purely infinite and not isomorphic to any Cuntz-Krieger algebra and Cuntz algebra. The subshift is called the context free shift. We will compute the topological entropy for the subshift and show that the KMS-state for the gauge action on the associated $C^*$-algebra exists if and only if the inverse temperature is $\log( 1 + \sqrt{1 + \sqrt{3}}) = 2.652\ldots = $ the topological entropy for the subshift, and the corresponding KMS-state is unique.

Keywords: Simple $C^*$-algebra, subshift, entropy, {\rm KMS}-state

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