von Neumann algebra factor
Algebras and modules
Model category presentations
Geometry on formal duals of algebras
Topics in Functional Analysis
For a von Neumann algebra write for its commutant in the ambient algebra of bounded operators.
A von Neumann algebra is called a factor if its center is trivial
Equivalently: if and its commutant generate the full algebra of bounded operators .
Every von Neumann algebra may be written as a direct integral? over factors. (von Neumann 49)
The original sources are
Lecture notes include
V.S. Sunder, von Neumann algebras, -factors, and their subfactors (pdf)
Hideki Kosaki, Type III factors and index theory (1993) (pdf)
The mathematics of inclusions of subfactors is giving deep structural insights. See also at planar algebra.
Index for subfactors, Invent. Math. 72, I (I983);
A polynomial invariant for links via von Neumann algebras, Bull. AMS 12, 103 (1985);
Hecke algebra representations of braid groups and link polynomials, Ann. Math. 126, 335 (1987)
Vaughan Jones, Scott Morrison, Noah Snyder, The classification of subfactors of index at most 5 (arXiv:1304.6141)
Vaughan F. R. Jones, David Penneys, Infinite index subfactors and the GICAR categories, arxiv/1410.0856
Relation to quantum field theory
Revised on June 13, 2016 15:31:49
by Urs Schreiber