Entropy for canonical shifts. II (Q1190734)

Let \(N\subset M\) be a pair of \(\sigma\)-finite factors. Given a conditional expectation \(E: M\to N\) with finite index, let \(A\) be the von Neumann algebra generated by the tower of relative commutants in the basic constructions iterated from \(E\). The authors define the canonical shifts \(\Gamma\) on \(A\) and study the entropy of \(\Gamma\) and the entropy of \(A\) relative to \(\Gamma(A)\), and also, their relationship with the minimum index \([M:N]_ 0\).