Timeline for How well is the classification of low-dimensional semisimple Hopf superalgebras (or braided Hopf algebras) understood?
Current License: CC BY-SA 4.0
8 events
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| May 16, 2019 at 16:36 | comment | added | Marco Farinati | sorry about the spelling! I was on my phone. "área guven" -> are given; Auch an element -> such an element ; should hice you ->should give you. Noe look if you hace --> Now look if you have. Sorry again | |
| May 16, 2019 at 16:30 | comment | added | Marco Farinati | I don't known the answer un general either, but I known the procedure. If you have an específic H in front of you (I thinking of being un front of the list of dim H leq60), compute the group-like elements. Most of the Hopf algebras un the classification tables área guven by generators that are group-like and skew primitives, so this part shouldn't be hard. Let g be Auch an element. If H=Ho#Z2 then evaluating g in 1 should hice you an álgebra mapa onto Ho. Noe look if you hace a Hopf subalgebra or not. | |
| May 16, 2019 at 16:22 | comment | added | Manuel Bärenz | Given an ordinary Hopf algebra $H_o$ of dimension $2n$, how many different Hopf super algebras $H$ are there such that $H \# k[\mathbb{Z}_2] \cong H_o$? That's not so easy to answer, I think. | |
| May 16, 2019 at 14:58 | comment | added | Marco Farinati | Well, is something like "do you know groups having $Z_2$ as semidirect factor, for small cardinal? I only found all groups of order less thanks 60". What I suggested is to look at known classification and look for those having a grouplike element of order 2. This is "some work", ok, but it is something, isn't? | |
| May 16, 2019 at 14:50 | review | Low quality posts | |||
| May 16, 2019 at 19:19 | |||||
| May 16, 2019 at 14:46 | comment | added | Alex M. | What the OP asks: "How well are low-dimensional Hopf superalgebras, that is, $\mathbb Z_2$-graded Hopf algebras or Hopf algebra objects internal to $\mathbb Z_2-\operatorname{Vect}$ understood? Up to which dimension are they classified? Are there interesting semisimple ones? Has someone worked out the representations?" What you answer: "with some work, one should get". | |
| May 16, 2019 at 14:25 | review | Late answers | |||
| May 16, 2019 at 14:46 | |||||
| May 16, 2019 at 14:07 | history | answered | Marco Farinati | CC BY-SA 4.0 |