### Divergence and super-divergence cocycles on the Grothendieck-Teichmueller Lie algebra

Alekseev, A *(Université de Genève)*

Monday 08 April 2013, 09:30-10:30

Seminar Room 1, Newton Institute

#### Abstract

The Grothendieck-Teichmueller Lie algebra grt can be viewed as a Lie subalgebra of derivations of the free Lie algebra in two generators. We use this observation to define two cocycles: the divergence cocycle on grt and the super-divergence cocycle on its even part. The divergence cocycle serves to define the Kashiwara-Vergne Lie algebra which is conjecturally isomorphic to grt. The super-divergence cocycle plays a role in the Rouviere's theory of symmetric spaces, and it is conjectured to be an injective map on the even part of grt.

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