TY - JOUR

T1 - Entropy of shifts on higher-rank graph C*-algebras.

AU - Skalski, Adam G.

AU - Zacharias, J.

N1 - Posted on the arXiv: 9th May 2006. To appear in Houston Journal of Mathematics; accepted in final form: 25th August 2006. RAE_import_type : Internet publication RAE_uoa_type : Pure Mathematics

PY - 2008/5/9

Y1 - 2008/5/9

N2 - Let OΛ be a higher-rank graph C*-algebra. For every p in Z+r there is a canonical completely positive map Φp on OΛ and a subshift Tp on the path space X=Λ∞. We show that ht(Φp)=h(Tp), where ht is Voiculescu's approximation entropy and h the classical topological entropy. For a higher rank Cuntz-Krieger algebra OM we obtain ht(Φp)= log rad(M1 p1... Mr pr), rad being the spectral radius. This generalizes Boca and Goldstein's result for Cuntz-Krieger algebras.

AB - Let OΛ be a higher-rank graph C*-algebra. For every p in Z+r there is a canonical completely positive map Φp on OΛ and a subshift Tp on the path space X=Λ∞. We show that ht(Φp)=h(Tp), where ht is Voiculescu's approximation entropy and h the classical topological entropy. For a higher rank Cuntz-Krieger algebra OM we obtain ht(Φp)= log rad(M1 p1... Mr pr), rad being the spectral radius. This generalizes Boca and Goldstein's result for Cuntz-Krieger algebras.

M3 - Journal article

VL - 34

SP - 269

EP - 282

JO - Houston Journal of Mathematics

JF - Houston Journal of Mathematics

IS - 1

ER -