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The first Hochschild (co)homology when adding arrows to a bound quiver algebra (1904.03565v2)
Published 7 Apr 2019 in math.KT and math.RT
Abstract: We provide a formula for the change of the dimension of the first Hoch-schild cohomology vector space of bound quiver algebras when adding new arrows. For this purpose we show that there exists a short exact sequence which relates the first cohomology vector spaces of the algebras to the first relative cohomology. Moreover, we show that the first Hochschild homologies are isomorphic when adding new arrows.