Geodesic
Compact group automorphisms, addition formulas and Fuglede-Kadison determinants
Hanfeng Li1
1 Department of Mathematics, Chongqing University, Chongqing, China and Department of Mathematics, SUNY at Buffalo, Buffalo, NY 14260-2900
Annals of mathematics, Tome 176 (2012) no. 1, pp. 303-347.

Voir la notice de l'article provenant de la source Annals of Mathematics website

For a countable amenable group $\Gamma$ and an element $f$ in the integral group ring $\mathbb{Z}\Gamma$ being invertible in the group von Neumann algebra of $\Gamma$, we show that the entropy of the shift action of $\Gamma$ on the Pontryagin dual of the quotient of $\mathbb{Z}\Gamma$ by its left ideal generated by $f$ is the logarithm of the Fuglede-Kadison determinant of $f$. For the proof, we establish an $\ell^p$-version of Rufus Bowen’s definition of topological entropy, addition formulas for group extensions of countable amenable group actions, and an approximation formula for the Fuglede-Kadison determinant of $f$ in terms of the determinants of perturbations of the compressions of $f$.
DOI : 10.4007/annals.2012.176.1.5

Hanfeng Li 1

1 Department of Mathematics, Chongqing University, Chongqing, China and Department of Mathematics, SUNY at Buffalo, Buffalo, NY 14260-2900 
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Hanfeng Li. Compact group automorphisms, addition formulas and Fuglede-Kadison determinants. Annals of mathematics, Tome 176 (2012) no. 1, pp. 303-347. doi : 10.4007/annals.2012.176.1.5. http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.176.1.5/

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