# Explicit Lie May structure on cosimplicial DG Lie algebras

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