Abstract
We describe the notion of the dimension group for subshifts in terms of symbolic dynamical system and show that the dimension group is a conjugacy invariant. We will show that the the hereditary subsets invariant under the dimension group automorphism exactly corresponds to the gauge invariant ideals of the associated -algebra for the subshift . As a result, we give the conditions that the -algebra becomes simple and purely infinite in terms of symbolic dynamics.
Citation
Kengo MATSUMOTO. "Dimension groups for subshifts and simplicity of the associated -algebras." J. Math. Soc. Japan 51 (3) 679 - 698, July, 1999. https://doi.org/10.2969/jmsj/05130679
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