The first cohomology group of the trivial extension of a monomial algebra
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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.
Final version to be published in Journal of Algebra and Its Applications (JAA). Small changes from previous version. 13 pages
Final version to be published in Journal of Algebra and Its Applications (JAA). Small changes from previous version. 13 pages