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Restricted Non‐Commutative Bernoulli Shifts
Author(s) -
Quasthoff Uwe
Publication year - 1990
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19901450118
Subject(s) - mathematics , bernoulli scheme , bernoulli's principle , ergodic theory , commutative property , equivalence (formal languages) , equivalence relation , measure (data warehouse) , pure mathematics , automorphism , sequence (biology) , invariant (physics) , discrete mathematics , database , biology , computer science , engineering , mathematical physics , genetics , aerospace engineering
Constructing non‐commutative Bernoulli shifts one starts with a measure theoretic Bernoulli shift and an equivalence relation on the measure space. There is a doubly infinite increasing sequence of measure preserving ergodic equivalence relations giving an increasing sequence of pairwise isomorphic von Neumann algebras invariant under the Bernoulli shift automorphism. We consider the index of Jones for those subalgebras and give an explicit example of conjugate non‐commutative Bernoulli shifts.