1106.5942 (Chris Heunen)

Characterizations of categories of commutative C*-subalgebras    [PDF]

Chris Heunen

We aim to characterize the category of injective *-homomorphisms between commutative C*-subalgebras of a given C*-algebra. We reduce this problem to finding a weakly terminal commutative subalgebra, and solve it for various C*-algebras, including all commutative ones and all type I von Neumann algebras. This answers a natural generalization of the Mackey--Piron programme: which lattices are those of closed subspaces of Hilbert space? We also discuss how the categorification differs from the original question.

View original: http://arxiv.org/abs/1106.5942