Advanced Search

The reconstruction algebra is a generalization of the preprojective algebra, and plays important roles in algebraic geometry and commutative algebra. We consider the homological property of this class of algebras by calculating the Hochschild homology and Hochschild cohomology. Let ${\Lambda }_t$ be the Yoneda algebra of a reconstruction algebra of type ${𝐀}_1$ over a field $.Inthispaper,aminimalprojectivebimoduleresolutionof$t$isconstructed,andthe$-dimensions of all Hochschild homology and cohomology groups of ${\Lambda }_t$ are calculated explicitly.