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

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Grothendieck-Teichmller Groups, Deformation and Operads

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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