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Fuglede-Kadison determinants and entropy for actions of discrete amenable groups

Author: Christopher Deninger
Journal: J. Amer. Math. Soc. 19 (2006), 737-758
MSC (2000): Primary 22D25, 37A35, 37B40, 46Lxx
Posted: February 6, 2006
MathSciNet review: 2220105
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Abstract | References | Similar Articles | Additional Information

Abstract: In 1990, Lind, Schmidt, and Ward gave a formula for the entropy of certain $\mathbb{Z}^n$ -dynamical systems attached to Laurent polynomials , in terms of the (logarithmic) Mahler measure of . We extend the expansive case of their result to the noncommutative setting where $\mathbb{Z}^n$ gets replaced by suitable discrete amenable groups. Generalizing the Mahler measure, Fuglede-Kadison determinants from the theory of group von Neumann algebras appear in the entropy formula.

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