$C^*$-algebras arising from substitutions

Details $C^*$-algebras arising from substitutions $C^*$-algebras arising from substitutions

2008-01-22

arxiv.org/abs/0801.3354v2

Mathematics

Operator Algebras

19 pages

Scientific paper

In this paper, we introduce a $C^{\ast}$-algebra associated with a proper
primitive substitution. We show that the $C^{\ast}$-algebra is simple and
purely infinite and contains the associated Cuntz-Krieger algebra and the
crossed product $C^{\ast}$-algebra of the corresponding Cantor minimal system.
We calculate the $K$-groups.

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