Characterizations of categories of commutative C*subalgebras
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If you have a question about this talk, please contact Julia Goedecke.
Piron’s problem in the foundations of quantum mechanics asks
which lattices are those of closed subspaces of Hilbert space. We
solve a natural categorification, by characterizing the category of
injective homomorphisms between commutative Csubalgebras of
various Calgebras, namely Calgebras of operators on separable
Hilbert spaces, any finitedimensional Calgebra, and any commutative
Calgebra. This is an important step in a promising ongoing approach
to a noncommutative generalisation of Gelfand’s duality between
compact Hausdorff spaces and commutative C*algebras, that we will
outline.
This talk is part of the Category Theory Seminar series.
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