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We describe how the Hochschild (co)homology of a bound quiver algebra changeswhen adding or deleting arrows to the quiver. The main tools are relativeHochschild (co)homology, the Jacobi-Zariski long exact sequence obtained by A.Kaygun and a one step relative projective resolution of a tensor algebra.

Deleting or adding arrows of a bound quiver algebra and Hochschild (co)homology