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

摘要

The paper [1] proved the Abramov-Rohlin addition formula and a version of Yuzvinskii’s addition formula for actions of free groups. The proofs have errors. We show here that the proof of the Abramov-Rohlin formula can be fixed with only a few minor modifications. We cannot fix the general proof of Yuzvinskii’s formula. However, in [2], we prove it under a mild technical condition for skew products with compact totally disconnected groups or compact finite dimensional Lie groups. We conjecture that the formula holds in complete generality. We also show that [1, Proposition 12.1] is incorrect and obtain a counterexample.