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• CommentRowNumber1.
• CommentAuthorMirco Richter
• CommentTimeFeb 25th 2012
• (edited Feb 25th 2012)

In

http://ncatlab.org/nlab/show/Lie+2-algebra, at

“… the differential respects the brackets: for all $x \in g_0$ and $h \in g_1$ we have

$\delta [x,h]=[x,\delta h]$

…”

is wrong. The equation should be:

$\delta \alpha(x,h) = [x,\delta h]$

Since I don’t know if I have the right to change an nLab entry,I post this here as an suggestion.

• CommentRowNumber2.
• CommentAuthorDavid_Corfield
• CommentTimeFeb 25th 2012

Change away. Everyone has the right. For a typo, no need to comment here. For a substantial change, leave a note at the forum.

• CommentRowNumber3.
• CommentAuthorMirco Richter
• CommentTimeFeb 25th 2012
done
• CommentRowNumber4.
• CommentAuthorjim_stasheff
• CommentTimeFeb 26th 2012
@

"...
the differential respects the brackets: for all
x∈g 0 and
h∈g 1 we have

δ[x,h]=[x,δh]

..."

is wrong. The equation should be:

δα(x,h)=[x,δh]

yes and no
1. it is common to denote $\alpha$ as [ , ]
2. in the context of respecting the brackets, it might be better to write

δ[x,h]= [δx,h]\pm [x,δh]
and then remark for h in ...
• CommentRowNumber5.
• CommentAuthorMirco Richter
• CommentTimeFeb 28th 2012
I agree on that, because the last equation is closer to the many bracket stuff of $L_\infty$-algebras.

But then the definition in the nLab entry must be changed (or another definition must be added), because in the entry as it is there is no defined bracket $[.,.]$ for elements of degree zero and one.
• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeFeb 28th 2012

there is no

Now there is.

• CommentRowNumber7.
• CommentAuthorMirco Richter
• CommentTimeFeb 28th 2012
• (edited Feb 28th 2012)

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