Timeline for The category of subfactors extending the category of groups?
Current License: CC BY-SA 3.0
16 events
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| Nov 3, 2014 at 21:30 | comment | added | Sebastien Palcoux | In this comment Fernando affirms (by writing << Yours too >>) that Mon$_{\mathcal{C}}$ has no zero object, nevertheless $_NN_N$ seems to be such a zero object. What do you think? | |
| Nov 3, 2014 at 21:10 | vote | accept | Sebastien Palcoux | ||
| Nov 1, 2014 at 14:46 | comment | added | Sebastien Palcoux | About your two last papers (here and there) with Kawahagashi, Longo and Rehren, are there videos or slides of talks, of you or of one of your collaborators? | |
| Nov 1, 2014 at 2:46 | comment | added | Marcel Bischoff | For the categorical definition see ncatlab.org/nlab/show/category+of+monoids | |
| Nov 1, 2014 at 2:39 | comment | added | Marcel Bischoff | see also here mathoverflow.net/questions/171840/… | |
| Nov 1, 2014 at 2:31 | comment | added | Marcel Bischoff | An algebra subobject is an intermediate subfactor. The condition for sub algebra objects etc., we reviewed here in the type III case. The projections should be the same as in the type II case here: arxiv.org/abs/1407.4793 I never really thought about morphisms besides injections.... | |
| Oct 31, 2014 at 0:32 | comment | added | Sebastien Palcoux | Here is a list of questions, can you enlighten some a them? : In the irreducible case, does an algebra subobject always correspond to an intermediate subfactor? Is there a reference for the definition of a morphism between algebra objects and also for a kernel? Do you know if the kernel of a morphism between algebra objects corresponds to a normal intermediate subfactor (and conversely)? Is it possible to quotient an algebra object by some algebra subobjects? Is there a definition for normal algebra subobjects? | |
| Oct 30, 2014 at 4:53 | comment | added | Marcel Bischoff | Note if you don't ask irreducibility you can have intermediate algebras which are not factors, eg. $N\subset N\oplus N \subset M_2(N)$, these do not correspond to simple algebra objects. | |
| Oct 30, 2014 at 4:51 | comment | added | Marcel Bischoff | Note if you don't ask irreducibility, then you can have | |
| Oct 30, 2014 at 4:49 | comment | added | Marcel Bischoff | Haploid means that ${}_NN_N \prec {}_NM_N$ has multiplicity one, which is equivalent with irreducibility. | |
| Oct 29, 2014 at 12:51 | comment | added | Sebastien Palcoux | In general, the $W^∗$-isomorphism of subfactors implies the isomorphism of planar algebras but the converse is false. I would like to see how the isomorphism of algebra objects is positioned relative to these two last isomorphisms. | |
| Oct 29, 2014 at 12:27 | comment | added | Sebastien Palcoux | What's your reference for haploid? | |
| Oct 29, 2014 at 12:22 | comment | added | Sebastien Palcoux | Very interesting! Before accepting your answer, I need to check that this definition is coherent with the definition of normal intermediate subfactor of T. Teruya (see a simplified definition here) as explained in the remark of my answer, and also I need to check by myself that $G \to A_G$ is really the natural expected functor from the category of finite groups to the category of (simple) algebra objects in $C$ (and extends to the category Kac algebras). | |
| Oct 29, 2014 at 2:33 | history | edited | Marcel Bischoff | CC BY-SA 3.0 |
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| Oct 29, 2014 at 2:25 | history | edited | Marcel Bischoff | CC BY-SA 3.0 |
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| Oct 29, 2014 at 2:20 | history | answered | Marcel Bischoff | CC BY-SA 3.0 |