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Shift Automorphisms of the Hyperfinite Factor
Author(s) -
Quasthoff Uwe
Publication year - 1987
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.19871310110
Subject(s) - automorphism , mathematics , conjugacy class , pure mathematics , measure (data warehouse) , entropy (arrow of time) , physics , quantum mechanics , database , computer science
For a large class of shift transformations of a L EBESGUE measure space (they have to fulfil some mixing condition) we construct automorphisms of the hyperfinite factor of type II 1 . The C ONNES ‐S TØRMER entropy of the resulting automorphisms equals the measure theoretic entropy of the corresponding shift transformations. Two such automorphisms are conjugate if the conjugacy between the original measure space shifts can be given by a code with finite expected code length.