Nonabelian free group actions: Markov processes, the Abramov-Rohlin formula and Yuzvinskii's formula

Details Nonabelian free group actions: Markov processes, the Abramov-Rohlin formula and Yuzvinskii's formula Nonabelian free group actions: Markov processes, the Abramov-Rohlin formula and Yuzvinskii's formula

2008-06-27

arxiv.org/abs/0806.4420v2

Mathematics

Dynamical Systems

39 pages. The introduction has been rewritten and minor errors corrected

Scientific paper

This paper introduces Markov chains and processes over nonabelian 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.

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