Open AccessCharacterizations of local Lie derivations on von Neumann algebras
Author(s) -
Guangyu An,
AUTHOR_ID,
Xueli Zhang,
Jun He,
Wenhua Qian,
AUTHOR_ID,
AUTHOR_ID
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022422
Subject(s) - von neumann architecture , mathematics , lie algebra , von neumann algebra , pure mathematics , lattice (music) , affiliated operator , algebra over a field , physics , jordan algebra , current algebra , acoustics
In this paper, we prove that every local Lie derivation on von Neumann algebras is a Lie derivation; and we show that if $ \mathcal M $ is a type I von Neumann algebra with an atomic lattice of projections, then every local Lie derivation on $ LS(\mathcal M) $ is a Lie derivation.