Researcher's Information
Structure analysis of von Neumann algebras
As we live in a three-dimensional world the idea of “fourdimensions” can be quite challenging but it is considered quite routine in mathematics, with well developed arguments for it in place. However, contrarily enough five-dimension or sixdimension worlds appear to have been taken for granted.
My interest is in the “infinite dimensional” world that could be considered to exist at the beyond of “finite-dimensional” worlds where phenomena considered impossible in a finite-dimensional world could occur. The subject of “operator algebras” can be considered something that “acts” on this marvelous world. The study of this is classified as “analysis”; however, it is also closely related to algebra and geometry. In the real world quantum mechanics and knot theory etc are also related to it.
This field is comparatively new in mathematics and has a lot of unknown problems, thus making it a challenging research subject.