Kadison-Singer algebras: hyperfinite case.
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- Record sourced from PubMed, PMID 20080617.
- Also identified by DOI 10.1073/pnas.0907161107 and PMC identifier 2836611.
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Abstract
A new class of operator algebras, Kadison-Singer algebras (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. A new invariant for the lattices is introduced to classify these algebras.