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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 language | English |
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Pages (from-to) | 215-238 |
Number of pages | 24 |
Journal | Communications in Mathematical Physics |
Volume | 331 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Oct 2014 |
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- 1 Finished