Timeline for Monoidal category of irreducible highest weight modules of the Virasoro algebra
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 26, 2019 at 14:42 | comment | added | Sebastien Palcoux | ncatlab.org/nlab/show/Frobenius-Perron+dimension | |
| Aug 26, 2019 at 14:23 | comment | added | soap | @SebastienPalcoux My motivation comes from physics (long story), since there is another monoidal category which is conjectured to be related to this category of irreps. (I do not know about that Perron-Frobenius dimension). I am a physicist with not that much (maybe not enough) knowledge about tensor categories the like) | |
| Aug 26, 2019 at 14:20 | comment | added | Sebastien Palcoux | No, it has not this property. But what is your motivation for such a property? If the tensor product of two irreps is still an irrep then the Perron-Frobenius dimension of every irrep should be $1$, and then the fusion category should be pointed (i.e. a deformation of a group), isn't it? What I wrote is for fusion categories; for the more general framework of monoidal categories, some confirmations are required... | |
| Aug 26, 2019 at 13:49 | comment | added | soap | @SebastienPalcoux I now realized that in your first comment you referred something that is probably my biggest concern: the tensor product of two irreducible representations will not be irreducible in general, as I wrote in my question. So I want a "new tensor product" for which the product of irreps is still an irrep. Do you know if that Connes fusion product has this property? | |
| Aug 24, 2019 at 13:10 | comment | added | Sebastien Palcoux | and yes, this answer should also help. | |
| Aug 24, 2019 at 12:55 | comment | added | Sebastien Palcoux | You will find a scan of Loke's thesis in this link. About mine, see Recall 12.39 and Theorem 12.46. | |
| Aug 24, 2019 at 12:24 | comment | added | soap | @SebastienPalcoux I did find your thesis, though. But on a first skim I only found comments about the category for the case of loop algebras, not the Virasoro algebra. Maybe I missed something? | |
| Aug 24, 2019 at 12:21 | comment | added | soap | @SebastienPalcoux This seems helpful, thank you. The link you provided does not contain the thesis itself, and I did not find it online. Is there a place where I can find the document? | |
| Aug 23, 2019 at 17:30 | comment | added | Sebastien Palcoux | I am not sure to understand what do you want, but usually the irreducible representations of some $\mathfrak{g}$ corresponds to the simple objects of $Rep(\mathfrak{g})$. So the tensor product of two simple objects is still an object of $Rep(\mathfrak{g})$. Now the monoidal category structure for such representations of $Vir$ was studied (in the Connes fusion framework) in the thesis of Terence Loke (and in mine for $Vir_{1/2}$). They are tensor product of $Rep$ of some loop algebras. | |
| Aug 23, 2019 at 12:11 | history | asked | soap | CC BY-SA 4.0 |