Dimension and dynamical entropy for metrized C*-algebras
Operator Algebras
2009-11-07 v1 Metric Geometry
Abstract
We introduce notions of dimension and dynamical entropy for unital C*-algebras ``metrized'' by means of c-Lip-norms, which are complex-scalar versions of the Lip-norms constitutive of Rieffel's compact quantum metric spaces. Our examples involve UHF algebras and noncommutative tori. In particular we show that the entropy of a noncommutative toral automorphism with respect to the canonical c-Lip-norm coincides with the topological entropy of its commutative analogue.
Keywords
Cite
@article{arxiv.math/0211043,
title = {Dimension and dynamical entropy for metrized C*-algebras},
author = {David Kerr},
journal= {arXiv preprint arXiv:math/0211043},
year = {2009}
}
Comments
To appear in Commun. Math. Phys., 33 pages