Timeline for Is there Z_n graded supersymmetry?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 12, 2021 at 12:52 | vote | accept | Olga | ||
| Jun 8, 2021 at 18:20 | comment | added | Steven Stadnicki | One magic word that might be some small help is 'anyon'; see e.g. arxiv.org/abs/1001.0274 . I'm not sure that this is quite aligned with your $\mathbb{Z}_n$ grading but it at least seems a close first cousin. | |
| Jun 8, 2021 at 17:07 | answer | added | Vladimir Dotsenko | timeline score: 2 | |
| Jun 8, 2021 at 15:00 | comment | added | Konstantinos Kanakoglou | To be more precise, i would tell that your $\alpha(r,p)$ is the bicharacter (or the color function) here. | |
| Jun 8, 2021 at 14:40 | answer | added | Konstantinos Kanakoglou | timeline score: 2 | |
| Jun 8, 2021 at 12:39 | comment | added | Olga | @KonstantinosKanakoglou I have added some explicit expressions for commutators and some more thoughts. I have never heard of bicharacters, but from what I've just skimmed through, the conditions on $\tilde{g}(i,l;j,k)$ are probably making it something similar, aren't they? | |
| Jun 8, 2021 at 12:30 | history | edited | Olga | CC BY-SA 4.0 |
added definitons of commutators
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| Jun 8, 2021 at 9:09 | comment | added | Konstantinos Kanakoglou | The commutation factor (which is the group bicharacter in the finite, abelian case) will also resolve your problem mentioned in the next paragraph (in the sense that it will allow to bypass the problem of being "bound" to the roots of unity case). | |
| Jun 8, 2021 at 9:07 | comment | added | Konstantinos Kanakoglou | The reason i am asking this, is that i suspect your resulting structure (spanned by $B$, $F$, $C$ now) is no more a Lie algebra but rather a $\mathbb{Z}_3$-graded, color Lie algebra -these, generalize the ordinary Lie algebras. And what is missing from your construction (if my understanding of what you are doing is correct) is the fact that once you go over to the $\mathbb{Z}_3$-grading, you also need to adopt a suitable color, that is a commutation factor or a bicharacter of the $\mathbb{Z}_3$ group for all this to work. | |
| Jun 8, 2021 at 9:03 | comment | added | Konstantinos Kanakoglou | One question regarding your approach: You say that you are adding an extra generator $C$ and you are using now $\mathbb{Z}_3$-graded commutators. How do you define (apart from the $\mathbb{Z}_3$-grading) the commutation relations with this new generator? I mean what are the exact relations? Because you are essentially changing your algebra like this. Is it still a Lie algebra ? | |
| Jun 8, 2021 at 3:48 | review | First posts | |||
| Jun 8, 2021 at 5:58 | |||||
| Jun 8, 2021 at 3:43 | history | asked | Olga | CC BY-SA 4.0 |