FugledeKadison determinants and entropy for actions of discrete amenable groups
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, FugledeKadison determinants from the theory of group von Neumann algebras appear in the entropy formula.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2005
 arXiv:
 arXiv:math/0502233
 Bibcode:
 2005math......2233D
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematics  Operator Algebras;
 22D25;
 37A35;
 37B40;
 46Lxx
 EPrint:
 27 pages