On the semisimplicity of the outer derivations of monomial algebras.

Selene Sanchez-Flores (1)

1 MI - Mathematisches Institut - Universität zu Köln

We show that the Hochschild cohomology of a monomial algebra over a field of characteristic zero vanishes from degree two if the first Hochschild cohomology is semisimple as a Lie algebra. We also prove that first Hochschild cohomology of a radical square zero algebra is reductive as a Lie algebra. In the case of the multiple loops quiver, we obtain the Lie algebra of square matrices of size equal to the number of loops.

Mots clés: Hochschild cohomology; outer derivations; Gerstenhaber bracket; monomial algebra; radical square zero algebra

Domaines: Anneaux et algèbres [math.RA]

Selene Sanchez-Flores. On the semisimplicity of the outer derivations of monomial algebras.. 2009. ⟨hal-00462467⟩