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arXiv · 1004.2820

On the semisimplicity of the outer derivations of monomial algebras

Selene Sanchez-Flores
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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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Selene Sanchez-Flores. 2010-04-16. On the semisimplicity of the outer derivations of monomial algebras. https://arxiv.org/abs/1004.2820

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