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Entropy for expansive algebraic actions of residually finite groups

  • LEWIS BOWEN (a1)
  • DOI:
  • Published online: 26 May 2010

We prove a formula for the sofic entropy of expansive principal algebraic actions of residually finite groups, extending recent work of Deninger and Schmidt.

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[4]L. Bowen . Measure conjugacy invariants for actions of countable sofic groups. J. Amer. Math. Soc. 23 (2010), 217245.

[5]C. Deninger . Fuglede–Kadison determinants and entropy for actions of discrete amenable groups. J. Amer. Math. Soc. 19 (2006), 737758.

[7]B. Fuglede and R. V. Kadison . Determinant theory in finite factors. Ann. of Math. (2) 55 (1952), 520530.

[8]A. S. Kechris . Global Aspects of Ergodic Group Actions (Mathematical Surveys and Monographs, 160). American Mathematical Society, Providence, RI, 2010.

[9]A. S. Kechris and T. Tsankov . Amenable actions and almost invariant sets. Proc. Amer. Math. Soc. 136(2) (2008), 687697 (electronic).

[10]V. Losert and H. Rindler . Almost invariant sets. Bull. London Math. Soc. 13(2) (1981), 145148.

[11]D. Lind , K. Schmidt and T. Ward . Mahler measure and entropy for commuting automorphisms of compact groups. Invent. Math. 101 (1990), 593629.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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