Compact group automorphisms, addition formulas and Fuglede-Kadison determinants
Copyright policy )Compact group automorphisms, addition formulas and Fuglede-Kadison determinants
For a countable amenable group ��and an element f in the integral group ring Z��being invertible in the group von Neumann algebra of ��, we show that the entropy of the shift action of ��on the Pontryagin dual of the quotient of Z��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.
To appear in Ann. of Math., 41 pages
- SUNY at Buffalo United States
- University at Buffalo, State University of New York United States
- Chongqing University China (People's Republic of)
Topological entropy, \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations, Mathematics - Operator Algebras, Dynamical Systems (math.DS), Measure-preserving transformations, 37B40, 37A35, 22D25, FOS: Mathematics, Entropy and other invariants, isomorphism, classification in ergodic theory, Mathematics - Dynamical Systems, entropy, Operator Algebras (math.OA), Fuglede-Kadison determinant, algebraic dynamics
Topological entropy, \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations, Mathematics - Operator Algebras, Dynamical Systems (math.DS), Measure-preserving transformations, 37B40, 37A35, 22D25, FOS: Mathematics, Entropy and other invariants, isomorphism, classification in ergodic theory, Mathematics - Dynamical Systems, entropy, Operator Algebras (math.OA), Fuglede-Kadison determinant, algebraic dynamics
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