Open AccessKadison–Singer algebras, II: General case
Author(s) -
Liming Ge,
Wei Yuan
Publication year - 2010
Publication title -
proceedings of the national academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.0914150107
Subject(s) - noncommutative geometry , centralizer and normalizer , affiliated operator , diagonal , von neumann architecture , mathematics , nest algebra , jordan algebra , pure mathematics , von neumann algebra , class (philosophy) , abelian von neumann algebra , non associative algebra , operator algebra , operator (biology) , matrix (chemical analysis) , algebra over a field , algebra representation , chemistry , computer science , geometry , transcription factor , gene , biochemistry , artificial intelligence , chromatography , repressor
A new class of operator algebras, Kadison-Singer (KS-) algebras, is introduced. These highly noncommutative, non self-adjoint algebras generalize triangular matrix algebras. They are determined by certain minimally generating lattices of projections in the von Neumann algebras corresponding to the commutant of the diagonals of the KS-algebras. It is shown that these lattices and their reduced forms are often homeomorphic to classical manifolds such as the sphere.
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