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On automorphisms of finite von Neumann algebras leaving invariant some reflexive lattices
Author(s) -
Wu Wenming,
Yuan Wei
Publication year - 2017
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12032
Subject(s) - mathematics , automorphism , invariant (physics) , automorphisms of the symmetric and alternating groups , pure mathematics , lattice (music) , von neumann architecture , reflexivity , mathematical physics , physics , social science , sociology , acoustics
For a fixed double triangle lattice in a finite factor, we show that the subgroup of automorphisms of the factor leaving invariant the reflexive lattice generated by the double triangle lattice is isomorphic to a closed subgroup of S O ( 3 ) . In particular, if the nontrivial projections in the lattice is free, then the group is explicitly determined as the symmetric group of 3 elements.
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