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The first cohomology group of the trivial extension of a monomial algebra

Claude Cibils·Maria Julia Redondo·Manuel Saorin
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Abstract

Given a finite--dimensional monomial algebra $A$ we consider the trivial extension $TA$ and provide formulae, depending on the characteristic of the field, for the dimensions of the summands $HH_1(A)$ and $\Alt(DA)$ of the first Hochschild cohomology group $HH^1(TA)$. From these a formula for the dimension of $HH^1(TA)$ can be derived.

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Claude Cibils, Maria Julia Redondo, Manuel Saorin. 2003-06-26. The first cohomology group of the trivial extension of a monomial algebra. https://arxiv.org/abs/math/0210284

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