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In the paper "Homotopy Lie algebras", Schechtman and Hinich proved that any cosimplicial differential graded Lie algebra has the structure of a 'Lie May algebra'.

If my understanding is right here, a Lie May algebra is just an uncommon term for Lie infinity algebra.

Now the question is, if there is any explicit construction of this Lie infinity algebra structure?

I mean, are there any explicit formulas that define the $k$-ary brackets of this Lie $\infty$-algebra in terms of the cofaces/codegeneracies and the Lie bracket of the underlying cosimplicial DG Lie algebra?

Edit: If this is unknown, then I would be thankful for ideas on how to proceed in an attempt to find these maps.

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Why doesn't the proof answer your question? – Fernando Muro May 3 '13 at 21:58
The proof uses the Lie Eilenberg Zilber operad and doesn't make any reference to the maps I'm after. If one can read the k-ary maps from the action of this operad on the cosimpl. DG Lie algebra, then this is not at all obvious... At least to me. – Nevermind May 3 '13 at 22:33
The authors of the paper in question are Vladimir Hinich and Vadim Schechtman, and they are responsible for the name ``Lie May''. My only real connection with the paper is that I wrote its Math Review. My recollection is that the L_{\infty} nomenclature came later. – Peter May May 4 '13 at 1:19
I mixed it up... Replaced 'May' by 'Schechtman' as author. Sorry for that. – Nevermind May 4 '13 at 1:41

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