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Dimension and Dynamical Entropy for Metrized C *-Algebras

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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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Authors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan. E-mail:dkerr@ms.u-tokyo.ac.jp, , , , , , JP

    David Kerr

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  1. David Kerr
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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

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