On the Semisimplicity of the Outer Derivations of Monomial Algebras |
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Authors: | Selene Sánchez-Flores |
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Institution: | 1. Mathematisches Institut , Universit?t zu K?ln , K?ln , Germany ssanchez@math.uni-koeln.de |
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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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Keywords: | Gerstenhaber bracket Hochschild cohomology Monomial algebra Outer derivations Radical square zero algebra |
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