Fuglede–Kadison determinants and entropy for actions of discrete amenable groups
Copyright policy )Fuglede–Kadison determinants and entropy for actions of discrete amenable groups
In 1990, Lind, Schmidt, and Ward gave a formula for the entropy of certain Z n \mathbb {Z}^n -dynamical systems attached to Laurent polynomials P P , in terms of the (logarithmic) Mahler measure of P P . We extend the expansive case of their result to the noncommutative setting where Z n \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.
- University of Münster Germany
37A35, Topological entropy, \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations, Fuglede-Kadison determinant, entropy, amenable group, 46Lxx, Means on groups, semigroups, etc.; amenable groups, Mathematics - Operator Algebras, 37B40, Dynamical Systems (math.DS), 22D25; 37A35; 37B40; 46Lxx, Mahler measure, FOS: Mathematics, 22D25, Entropy and other invariants, isomorphism, classification in ergodic theory, Mathematics - Dynamical Systems, Noncommutative dynamical systems, Operator Algebras (math.OA)
37A35, Topological entropy, \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations, Fuglede-Kadison determinant, entropy, amenable group, 46Lxx, Means on groups, semigroups, etc.; amenable groups, Mathematics - Operator Algebras, 37B40, Dynamical Systems (math.DS), 22D25; 37A35; 37B40; 46Lxx, Mahler measure, FOS: Mathematics, 22D25, Entropy and other invariants, isomorphism, classification in ergodic theory, Mathematics - Dynamical Systems, Noncommutative dynamical systems, Operator Algebras (math.OA)
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