A periodisation of semisimple Lie algebras.

Larsson, Anna

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The knowledge of the natural graded algebras of a given class of Lie algebras offers essential information about the structure of the class. So far, the classification of naturally graded Lie algebras is only known for some families of p-filiform Lie algebras. In certain sense, if g is a naturally graded Lie algebra of dimension n, the first case of no p-filiform Lie algebras it happens when the characteristic sequence is (n-3,2,1). We present the classification of a particular family...

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Let $M$ be a differential manifold. Let $Φ$ be a Drinfeld associator. In this paper we explain how to construct a global formality morphism starting from $Φ$ . More precisely, following Tamarkin’s proof, we construct a Lie homomorphism “up to homotopy" between the Lie algebra of Hochschild cochains on $C^{\infty} (M)$ and its cohomology $(Γ (M, Λ T M), {[-, -]}_{S}$ ). This paper is an extended version of a course given 8 - 12 March 2004 on Tamarkin’s works. The reader will find explicit examples, recollections on $G_{\infty}$ -structures, explanation...