Non-abelian free group actions: Markov processes, the Abramov–Rohlin formula and Yuzvinskii’s formula-Reference-Cited by-同舟云学术

Non-abelian free group actions: Markov processes, the Abramov–Rohlin formula and Yuzvinskii’s formula

Published:2009-10-13 Issue:6 Volume:30 Page:1629-1663
ISSN:0143-3857
Container-title:Ergodic Theory and Dynamical Systems
language:en
Short-container-title:Ergod. Th. Dynam. Sys.

Author:

BOWEN LEWIS

Abstract

AbstractThis paper introduces Markov chains and processes over non-abelian free groups and semigroups. We prove a formula for the f-invariant of a Markov chain over a free group in terms of transition matrices that parallels the classical formula for the entropy a Markov chain. Applications include free group analogues of the Abramov–Rohlin formula for skew-product actions and Yuzvinskii’s addition formula for algebraic actions.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,General Mathematics

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