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Keywords:
Hochschild cohomology; reconstruction algebra; Yoneda algebra
Summary:
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 ${\mathbf {A}}_{1}$ over a field $\k $. In this paper, a minimal projective bimodule resolution of $\Lambda _{t}$ is constructed, and the $\k $-dimensions of all Hochschild homology and cohomology groups of $\Lambda _{t}$ are calculated explicitly.
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