Abstract:
We introduce notions of dimension and dynamical entropy for unital C *-algebras ``metrized'' by means of , which are complex-scalar versions of the Lip-norms constitutive of Rieffel's compact quantum metric spaces. Our examples involve the UHF algebras and noncommutative tori. In particular we show that the entropy of a noncommutative toral automorphism with respect to the canonical coincides with the topological entropy of its commutative analogue.
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Received: 13 February 2002 / Accepted: 20 August 2002 Published online: 22 November 2002
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Kerr, D. Dimension and Dynamical Entropy for Metrized C *-Algebras. Commun. Math. Phys. 232, 501–534 (2003). https://doi.org/10.1007/s00220-002-0741-0
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DOI: https://doi.org/10.1007/s00220-002-0741-0