$C^{\ast }$-algebras arising from substitutions

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.

19 pages