Dimension and dynamical entropy for metrized C*-algebras

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.

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

References in corpus (5)

• Gravity coupled with matter and foundation of non-commutative geometry
• Metrics on State Spaces
• Metrics on states from actions of compact groups
• Gromov-Hausdorff Distance for Quantum Metric Spaces
• Quantized chaotic dynamics and non-commutative KS entropy

Cited by in corpus (3)

• Matricial quantum Gromov-Hausdorff distance
• $L^p$-spectral triples and $p$-quantum compact metric spaces
• Lipschitzness of *-homomorphisms between C*-metric algebras