Timeline for Calculation of Dynkin operator on free Lie rings
Current License: CC BY-SA 4.0
18 events
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| May 4, 2019 at 16:01 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Apr 4, 2019 at 15:49 | answer | added | Siddhartha | timeline score: 1 | |
| Apr 1, 2019 at 8:03 | comment | added | Duchamp Gérard H. E. | Maybe it is erroneous because in free Lie rings, we don't have the identity $[[X,Y],[Z,T]]$ equals $[X,Y],Z],T]]]$. In fact, to construct the Dynkin projector, the crucial step is to show that $w\to [w]$ is a derivation of $Li_\mathbb{Z}(X)$ where $X$ is an alphabet and $Li_\mathbb{Z}(X)(\subset \mathbb{Z}<X>)$ the module of Lie polynomials. | |
| Mar 31, 2019 at 20:06 | comment | added | YCor | "left-normed": $[x_1,\dots,x_k]=[[x_1,\dots,x_{k-1}],x_k]$. | |
| Mar 31, 2019 at 19:41 | comment | added | Siddhartha | It is left normed. | |
| Mar 31, 2019 at 19:24 | comment | added | YCor | Maybe also recall the convention for multiple brackets: $[x_1,\dots,x_k]$ is defined as $[x_1,[x_2,\dots,x_k]]$ or as $[[x_1,\dots,x_{k-1}],x_k]$? | |
| Mar 31, 2019 at 19:23 | comment | added | Siddhartha | Not really. Let's assume $A$ is non-unital for time being. | |
| Mar 31, 2019 at 19:22 | comment | added | YCor | OK; I now get the definition (technically I don't know if you assume $A$ unital, in which case you have to define $\delta(1)$, probably by $\delta(1)=0$; anyway this does not matter for the question). | |
| Mar 31, 2019 at 19:20 | history | edited | YCor |
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| Mar 31, 2019 at 19:20 | comment | added | Siddhartha | Thanks. Edited now. | |
| Mar 31, 2019 at 19:20 | history | edited | Siddhartha | CC BY-SA 4.0 |
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| Mar 31, 2019 at 19:19 | comment | added | YCor | So it's just "associative monomials", nothing Lie. | |
| Mar 31, 2019 at 19:18 | comment | added | Siddhartha | Products of the form $x_{i_1} \dotsc x_{i_m}$ where the variables need not be commutative, but these are associative. | |
| Mar 31, 2019 at 19:17 | comment | added | YCor | What do you mean by "associative Lie monomials"? | |
| Mar 31, 2019 at 19:15 | history | edited | Siddhartha | CC BY-SA 4.0 |
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| Mar 31, 2019 at 19:08 | history | edited | YCor |
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| Mar 31, 2019 at 19:07 | comment | added | YCor | I have no idea how you define $\delta$, and even how it is supposed to be an operator from which space to which other space (maybe the free Lie ring to itself). | |
| Mar 31, 2019 at 19:00 | history | asked | Siddhartha | CC BY-SA 4.0 |