Timeline for Quantum sheaves
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Nov 10, 2021 at 18:50 | history | edited | Vanessa | CC BY-SA 4.0 |
edited body
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| Nov 28, 2011 at 11:13 | comment | added | Chris Heunen | Instead of closed subspaces of a Hilbert space, you can phrase this in terms of closed ideals of the Von Neumann algebra of bounded operators on $H$. If you add the condition that a quantum topology must be closed under (pointwise) composition of operators, then it looks like you're asking for a sheaf on a quantale, for which there are various proposals; see e.g. [Borceux & Van den Bossche, Order 3:61--87, 1986]. | |
| Nov 26, 2011 at 22:47 | history | edited | Yemon Choi |
added category theory tag
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| Nov 26, 2011 at 22:17 | comment | added | alexod | In arxiv.org/abs/0709.4364 Heunen, Landsman and Splitters construct a sheaf over a C*-algebras for quantum logic. But I don't know whether their construction differs from your definition. | |
| Nov 26, 2011 at 22:16 | comment | added | Yemon Choi | Are you assuming that all the $s(V)$ are realized on the same Hilbert space? (If not, then it would seem more natural to talk of $s$ as being a functor from the poset $\Sigma$ to the category of $C*$-algebras and $*$-homomorphisms) | |
| Nov 26, 2011 at 21:49 | history | asked | Vanessa | CC BY-SA 3.0 |