$C^*$-algebras arising from substitutions

Masaru Fujino

$C^*$-algebras arising from substitutions

Operator Algebras 2008-06-26 v2 Dynamical Systems

Authors: Masaru Fujino

Abstract

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.

Keywords

graph algebras c*-algebras cuntz semigroup

Cite

@article{arxiv.0801.3354,
  title  = {$C^*$-algebras arising from substitutions},
  author = {Masaru Fujino},
  journal= {arXiv preprint arXiv:0801.3354},
  year   = {2008}
}

Comments

19 pages

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