X-Nico

unusual facts about von Neumann algebras



Vaughan Jones

His work on knot polynomials, with the discovery of what is now called the Jones polynomial, was from an unexpected direction with origins in the theory of von Neumann algebras, an area of analysis already much developed by Alain Connes.


see also

Commutation theorem

It was not until the late 1960s, prompted partly by results in algebraic quantum field theory and quantum statistical mechanics due to the school of Rudolf Haag, that the more general non-tracial Tomita–Takesaki theory was developed, heralding a new era in the theory of von Neumann algebras.

Finite dimensional von Neumann algebra

The finite dimensional case differs from the general von Neumann algebras in that topology plays no role and they can be characterized using Wedderburn's theory of semisimple algebras.