Geodesic
Fuglede–Kadison determinants and entropy for actions of discrete amenable groups
Deninger, Christopher1
1Mathematisches Institut, Universität Münster, Einsteinstrasse 62, 48149 Münster, Germany
Journal of the American Mathematical Society, Tome 19 (2006) no. 3, pp. 737-758

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S0894-0347-06-00519-4

Deninger, Christopher  1

1 Mathematisches Institut, Universität Münster, Einsteinstrasse 62, 48149 Münster, Germany 
Deninger, Christopher. Fuglede–Kadison determinants and entropy for actions of discrete amenable groups. Journal of the American Mathematical Society, Tome 19 (2006) no. 3, pp. 737-758. doi: 10.1090/S0894-0347-06-00519-4
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