The Lie module structure on the Hochschild cohomology groups of monomial algebras with radical square zero.

Selene Sanchez-Flores (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We study the Lie module structure given by the Gerstenhaber bracket on the Hochschild cohomology groups of a monomial algebra with radical square zero. The description of such Lie module structure will be given in terms of the combinatorics of the quiver. The Lie module structure will be related to the classification of finite dimensional modules over simple Lie algebras when the quiver is given by the two loops and the ground field is the complex numbers.

Mots clés: Hochschild cohomology; Lie; monomial; Gerstenhaber

Domaines: Théorie des représentations [math.RT]

Selene Sanchez-Flores. The Lie module structure on the Hochschild cohomology groups of monomial algebras with radical square zero.. 2008. ⟨hal-00188442v2⟩