Characterizations of categories of commutative C*-subalgebras
Operator Algebras
2016-12-02 v3 Category Theory
Quantum Physics
Abstract
We aim to characterize the category of injective *-homomorphisms between commutative C*-subalgebras of a given C*-algebra A. We reduce this problem to finding a weakly terminal commutative subalgebra of A, and solve the latter for various C*-algebras, including all commutative ones and all type I von Neumann algebras. This addresses a natural generalization of the Mackey-Piron programme: which lattices are those of closed subspaces of Hilbert space? We also discuss the way this categorified generalization differs from the original question.
Keywords
Cite
@article{arxiv.1106.5942,
title = {Characterizations of categories of commutative C*-subalgebras},
author = {Chris Heunen},
journal= {arXiv preprint arXiv:1106.5942},
year = {2016}
}
Comments
24 pages