Abstract:We study the deformation complex of the standard morphism from the degree d shifted Lie operad to its polydifferential version, and prove that it is quasi-isomorphic to the Kontsevich graph complex GC d . In particular, we show that in the case d = 2 the Grothendieck-Teichmüller group GRT 1 is a symmetry group (up to homotopy) of the aforementioned morphism. We also prove that in the case d = 1 corresponding to the usual Lie algebras the standard morphism admits a unique homotopy non-trivial deformation which … Show more
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