Hochschild (co)homology of Yoneda algebras of reconstruction algebras of type ${\mathbf{A}}_1$

Czechoslovak Mathematical Journal

Bo Hou¹ 

[1] Yanhong Guo, School of Mathematics and Statistics, Henan University, No. 1, Jinming Avenue, Kaifeng 475004, Henan, P. R. China

关键词: Hochschild cohomology;    reconstruction algebra;    Yoneda algebra;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

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.

【 授权许可】

Unknown