Characterizations of Categories of Commutative C*-Subalgebras

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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.
Original languageEnglish
Pages (from-to)215-238
Number of pages24
JournalCommunications in Mathematical Physics
Volume331
Issue number1
DOIs
Publication statusPublished - 1 Oct 2014

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