Séminaire de Mathématique
# Cours -- Symmetries of Poisson Brackets: The Graph Complex and Orientation Morphism

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Amphithéâtre Léon Motchane (IHES)
### Amphithéâtre Léon Motchane

#### IHES

Le Bois Marie
35, route de Chartres
91440 Bures-sur-Yvette

Description

Lecture 3

The graph orientation morphism: constructing a symmetry by using a graph cocycle.

* Endomorphisms of the space of multivector fields. The Schouten bracket, its own Jacobi identity; the master-equation. The Richardson--Nijenhuis bracket, its own Jacobi identity; the master equation.

* The edge (the stick in the construction of graph differential). The graph orientation morphism Or takes the stick to the Schouten bracket.

* Verifying the property of the image of a graph cocycle under Or to be a Poisson cocycle. Canonical and incidental solutions of the problem of factorization via the Jacobiator. Topological identities in the spaces of Leibniz graphs.

* Lie algebra homomorphism: from graph cocycles to symmetries of Poisson brackets.

Organized by

Maxim Kontsevich

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