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Theses

Crochet de Gerstenhaber pour les algèbres enveloppantes d'algèbres de Lie de dimension finie

Abstract : In this thesis, we explicitly describe the multiplicative structure and the graded Lie algebra structure of the cohomology of finite-dimensional Lie algebras. In a first step, we introduce a multiplicative structure for the cohomology of Lie algebra. Then, we explicitly show that there exists an isomorphism of commutative graded algebras between the Hochschild cohomology algebra of the enveloping algebra provided with the cup product and the cohomology algebra of the Lie algebra. In a second step, we introduce a graded Lie algebra structure for the cohomology of Lie algebra. Then, we show that there exists an isomorphism of graded Lie algebras between the Hochschild cohomology Lie algebra of the enveloping algebra provided with the Gerstenhaber bracket and the cohomology algebra of the Lie algebra. Finally, we describe completely the Gerstenhaber bracket on the Hochschild cohomology of the enveloping algebra of a Lie algebra for dimension _ 3.
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  • HAL Id : tel-01725219, version 1

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Rabih Bou Daher. Crochet de Gerstenhaber pour les algèbres enveloppantes d'algèbres de Lie de dimension finie. Algèbre commutative [math.AC]. Université Clermont Auvergne, 2017. Français. ⟨NNT : 2017CLFAC039⟩. ⟨tel-01725219⟩

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