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

Christopher Deninger
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Abstract

In 1990, Lind, Schmidt and Ward gave a formula for the entropy of certain $\mathbb{Z}^n$-dynamical systems attached to Laurent polynomials $P$, in terms of the (logarithmic) Mahler measure of $P$. 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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Christopher Deninger. 2005-02-11. Fuglede-Kadison determinants and entropy for actions of discrete amenable groups. https://arxiv.org/abs/math/0502233

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