Timeline for Quasi-Lie algebras in nature?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Mar 31, 2011 at 21:30 | comment | added | Jim Conant | @Daniel: But $[x,[x,x]]=0$ by the Jacobi identity! I guess in the super case, if $x$ has odd degree, this would be $3$-torsion. | |
| Mar 31, 2011 at 20:43 | comment | added | Daniel Moskovich | @Jim: I suspect the 3-torsion is coming from 3[x,[x,x]]=0 by the Jacobi relation. | |
| Mar 13, 2011 at 13:33 | comment | added | Jim Conant | @Mariano: Thanks for the dictionary translating Hilton's terms into modern ones. I have to admit I didn't read it carefully, mainly because he finds both 2 and 3-torsion in the free quasi Lie ring, whereas there is only 2-torsion in Levine's free quasi-Lie algebra. So I concluded they are not the same definition. I think you are right that taking $M=0$ in Hilton's definition does give you a quasi Lie algebra in Levine's sense, although I'm still unsure where that 3-torsion is coming from. | |
| Mar 13, 2011 at 7:19 | comment | added | Mariano Suárez-Álvarez | @Jim: maybe there is something I am not seeing... but Hilton's motivating example is precisely the homotopy groups with the Whitehead bracket. Since he wants to consider all the groups (and since he is writing before super became a word), he defines quasi-Lie rings as pairs $(A,M)$, which in the case of the homotopy groups end up being $A$ the odd homotopy groups and $M$ the even homotopy groups, but it is clear that if $(A,M)$ is such an object, then $(A,0)$ is too, and that is the same thing as considering only the odd groups. | |
| Mar 13, 2011 at 1:54 | comment | added | Jim Conant | Tom gave a perfectly fine answer, so I'm posting it as a community wiki and accepting it. | |
| Mar 13, 2011 at 1:53 | vote | accept | Jim Conant | ||
| Mar 13, 2011 at 1:53 | history | bounty ended | Jim Conant | ||
| Mar 13, 2011 at 1:53 | history | answered | Jim Conant | CC BY-SA 2.5 |