On the semisimplicity of the outer derivations of monomial algebras

2010/04/16 by Sanchez-Flores, Selene
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1004.2820

Abstract

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.

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