Looks good. Thanks!

]]>I corrected the aforementioned error. This is my first edit, so I hope I haven’t broken anything.

]]>I don’t have the leisure to check now. But if/where it has “$n+1$” when it should read “$n$” and you are sure you know what you are doing: Please just fix it! (Just hit “edit” at the bottom of the page).

]]>The statement of the strong homotopy Jacobi identity contains some errors. Note that there are $n$ $v$’s in the equation. This is correct, since a composition of $l_j$ with $l_i$ should take $n=i+j-1$ arguments. For this reason, it should say “for all $n$-tuples” (not $n+1$). I believe the inner sum should be over $(i,j-1)$-unshuffles, since $(i,j)$-unshuffles would permute $n+1$ objects.

A similar error occurs when Loday and Valette try to state this identity for the operad. I am actually struggling to find the correct identity written down with signs anywhere.

]]>I have added the reference for the survey posted today on arxiv by Stasheff, but am not sure if the formatting (that I used in editing this article) is appropriate.

Anonymous

]]>added references Buijs-Felix-Murillo 12 and Buijs-Murillo 12 on $L_\infty$-algebras as models for rational homotopy theory

]]>added a remark (here) amplifying the ind-conilpotency of $CE_\bullet(\mathfrak{g})$

]]>I have polished a little the section *Definition – In terms of higher brackets*, at *L-infinity algebra*.

And in the section *In terms of semifree differential coalgebra* I have added text at the beginning highlighting that this reformulation was shown already in the original articles on $L_\infty$-algebras.

Here are now the slides from Jim’s talk yesterday: Stasheff 16.

Jim asks me to add that a more complete preprint is in preparation, and that meanwhile comments on the slides are most welcome.

]]>Together with Jim Stasheff (via email) we have been further expanding the list of references for $L_\infty$-algebras in physics.

For ease of editing and linking, I have now split it off as a separate entry *L-infinity algebras in physics*.

Jim Stasheff suggested that the entry *L-infinity algebra* ought to contain discussion of literature of $L_\infty$-algebras appearing in physics. I gather he would like to use such a list for his talk at “Higher structures in geometry and physics” in Bonn next week. Since we didn’t have such a list yet, I have now added one. Naturally the examples that come to my mind tend to be those that I have worked on myself. Please feel invited to add more.

I have substantially polished the section *Definition – In terms of higher brackets*.

Okay, I have filled in the signs of the “$L_\infty$-Jacobi identity” and then added a further section

Reformulation in terms of semifree dg-algebra – Details with an explicit pedestrian walk through the proof that an $L_\infty$-algebra structure on $\mathfrak{g}$ is the same as a dg-algebra structure on $\wedge \mathfrak{g}^*$ (for the degreewise finite dimensional case).

]]>Since it says “$\mathbb{N}_+$-graded” it’s shifted, hence “graded-symmetric” is correct.

Maybe I find the time to expand and polish the whole entry. Or maybe somebody else does.

]]>I don't have time to check whether you are writing at the level of the underlying gr vector space

or at the Chevalley Eilenberg shifted level

graded symmetric is fine after the shift

graded skew-symmetric at the unshifted level ]]>

I have changed at L-infinity algebra the “skew symmetric” brackets to “graded-symmetric”, for clarity.

I am having an email exchange with somebody trying to learn the basics of $L_\infty$-algebras. This highlights what is of course evident: the whole discussion here could do with more examples and more details.

I don’t have the time to look into this. But maybe I can convince my correspondent to include discussion of his newly gained insights into the $n$Lab entry, for the sake of those students coming after him…

]]>Urs, do you have any thoughts in the parallel discussion on the very related question I opened under Magnus infinity algebra ?

]]>I have finally added the statement that every $L_\infty$-algebra is quasi-isomorphic to a dg-Lie algebra (in char 0), together with a pointer to Kriz-May. Also at dg-Lie algebra

]]>expanded L-infinity-algebra as indicated on the nCafe, here

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