Dimension and dynamical entropy for metrized C*-algebras

Details Dimension and dynamical entropy for metrized C*-algebras Dimension and dynamical entropy for metrized C*-algebras

2002-11-04

arxiv.org/abs/math/0211043v1

Mathematics

Operator Algebras

To appear in Commun. Math. Phys., 33 pages

Scientific paper

10.1007/s00220-002-0741-0

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.

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