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Theses

The Lie structure on the Hochschild cohomology d'algèbres monomiales.

Abstract : This thesis is about the Lie structure on the Hochschild cohomology, given by the Gerstenhaber bracket. More precisely, we study the Lie algebra structure of the first Hochschild cohomology group and the Lie module structure of the Hochschild cohomology groups of some monomial algebras. The aim of this thesis is to study the Lie structure on the Hochschild cohomology of finite-dimensional monomial algebras. A monomial algebra is defined as the quotient of the path algebra of a quiver by a two-sided admissible ideal generated by a set of paths of length at least two. We use the intrinsic combinatorial data of such algebras to study the Lie structure defined on the Hochschild cohomology by the Gerstenhaber bracket. Actually, we discuss two aspects of such algebraic structure. The first one is the relationship between semi-simplicity on the first Hochschild cohomology group and the vanishing of the Hochschild cohomology groups. In the second one, we center our attention to the Lie module structure of the Hochschild cohomology groups of a particular family of monomial algebras: those whose Jacobson radical square is zero
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https://tel.archives-ouvertes.fr/tel-00464064
Contributor : Selene Sanchez-Flores <>
Submitted on : Monday, March 15, 2010 - 6:08:40 PM
Last modification on : Thursday, January 11, 2018 - 6:15:40 AM
Long-term archiving on: : Friday, October 19, 2012 - 9:50:38 AM

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  • HAL Id : tel-00464064, version 1

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Selene Sanchez-Flores. The Lie structure on the Hochschild cohomology d'algèbres monomiales.. Mathematics [math]. Université Montpellier II - Sciences et Techniques du Languedoc, 2009. English. ⟨tel-00464064⟩

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