Entropy for expansive algebraic actions of residually finite groups

By Lewis Bowen. Ergodic Theory and Dynamical Systems, 2009

57 citations recorded by the source corpus.

Abstract We prove a formula for the sofic entropy of expansive principal algebraic actions of residually finite groups, extending recent work of Deninger and Schmidt.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6469faffb13e546c729f42e8303884016e5f79fe

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Homoclinic groups, IE groups, and expansive algebraic actions (2011, unknown): “D S] 2 J an 2 01”
Combinatorial Independence and Sofic Entropy (2012, background): “In line with previous work on algebraic actions [7, 10, 29, 34] (see also the more recent [30]), this value turns out to be equal to the logarithm of the Fuglede-Kadison determinant of f in the group von Neumann algebra LG.”
Compact Group Automorphisms, Addition Formulas and Fuglede-Kadison Determinants (2010, background): “For a countable residually finite (not necessarily amenable) group Γ and an f ∈ ZΓ, when the sofic approximation sequence of Γ comes from a sequence of finite-index normal subgroups of Γ, in various cases it has been shown that the sofic topological entropy and the sofic measure entropy (for the nor”
ENTROPY, DETERMINANTS, AND L 2 -TORSION (2012, background): “2 for countable residually finite groups has been established for some special cases in [6], [7], [36], though the general case is still open.”
Fuglede–Kadison Determinants and Sofic Entropy (2014, background): “1 in [6]), as well as Lewis Bowen and Hanfeng Li (see [9] Lemma 7.”