The Lie algebra structure of the first Hochschild cohomology group for monomial algebras

Claudia Strametz

doi:10.1016/S1631-073X(02)02346-4

The Lie algebra structure of the first Hochschild cohomology group for monomial algebras
[La structure d'algèbre de Lie du premier groupe de la cohomologie de Hochschild pour des algèbres monomiales]

Claudia Strametz ¹

¹ Laboratoire GTA UMR 5030, Département de Mathématiques, Université de Montpellier 2, 34095 Montpellier cedex 5, France

Comptes Rendus. Mathématique, Volume 334 (2002) no. 9, pp. 733-738.

Résumé
Abstract

Nous étudions la structure d'algèbre de Lie du premier groupe de la cohomologie de Hochschild d'une algèbre monomiale de dimension finie Λ, en termes combinatoires de son carquois, en quelconque caractéristique. Cela nous permet aussi d'examiner la composante de l'identité du groupe algébrique des automorphismes extérieurs de Λ en caractéristique zéro. Nous donnons des critères pour la résolubilité, la (semi-)simplicité, la commutativité et la nilpotence.

We study the Lie algebra structure of the first Hochschild cohomology group of a finite dimensional monomial algebra Λ, in terms of the combinatorics of its quiver, in any characteristic. This allows us also to examine the identity component of the algebraic group of outer automorphisms of Λ in characteristic zero. Criteria for the solvability, the (semi-) simplicity, the commutativity and the nilpotency are given.

Reçu le : 2002-01-21
Accepté le : 2002-03-04
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02346-4

Affiliations des auteurs :

Claudia Strametz ¹

¹ Laboratoire GTA UMR 5030, Département de Mathématiques, Université de Montpellier 2, 34095 Montpellier cedex 5, France

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     title = {The {Lie} algebra structure of the first {Hochschild} cohomology group for monomial algebras},
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Claudia Strametz. The Lie algebra structure of the first Hochschild cohomology group for monomial algebras. Comptes Rendus. Mathématique, Volume 334 (2002) no. 9, pp. 733-738. doi : 10.1016/S1631-073X(02)02346-4. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02346-4/

Bibliographie
Cité par

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[8] C. Strametz, The Lie algebra structure on the first Hochschild cohomology group of a monomial algebra, see | arXiv

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