Timeline for Non-commutative duality I: Which C*-algebras are (isomorphic to a) convolution algebra?
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| Oct 5, 2020 at 21:35 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
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| Oct 4, 2020 at 21:19 | comment | added | Nicola Ciccoli | 3. different choices of polarization results in different quotient groupoids. In some cases you can understand the relation between such groupoids as a Fourier transform. | |
| Oct 4, 2020 at 21:18 | comment | added | Nicola Ciccoli | 2. You choose polarization, i.e.a Lagrangian distribution with the additional property that the space of leaves inherits a groupoid structure. The quotient map is now only topological. | |
| Oct 4, 2020 at 18:28 | comment | added | Mirco A. Mannucci | PS I looked into your profile and I found a question of yours which is EXTREMELY relevant to me, namely the functoriality of the C*algebra for the cat of graphs.... | |
| Oct 4, 2020 at 18:16 | comment | added | Mirco A. Mannucci | so, 1) one starts from a (classical ) Poisson Manifold and its simplectic groupoid so far, so good. Now I am already lost: 2) you build a quotient groupoid (of the first one) which is only topological . I do not understand how that is done, and need clarification. I assume that , assuming the second groupoid is done, 3 ) one looks at TWO C* algebra, one from groupoid 1 and the other from its quotient. If I follow you, there is a (knd of) Fourier transform between these two. | |
| Oct 4, 2020 at 18:10 | comment | added | Mirco A. Mannucci | first of all, thanks for your contribution! here the horizons expand, and that is a good thing. But I want to understand, and, to this effect, I would ask you to schematize what you have said. I do not mean to add technicalities, proofs, etc. Only the key passages. Let me start and then you correct me, and/or fill the details. | |
| Oct 4, 2020 at 17:41 | history | answered | Nicola Ciccoli | CC BY-SA 4.0 |