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Chris Heunen, Oxford
Thursday 12 January 2012, 14:15-15:15
Characterizations of categories of commutative C*-subalgebras
- đ¤ Speaker: Chris Heunen, Oxford
- đ Date & Time: Thursday 12 January 2012, 14:15 - 15:15
- đ Venue: MR5, Centre for Mathematical Sciences
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Julia Goedecke
Abstract
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 C-subalgebras of various C-algebras, namely C-algebras of operators on separable Hilbert spaces, any finite-dimensional C-algebra, and any commutative C-algebra. 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.
Series This talk is part of the Category Theory Seminar series.
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