粘合箭线下的Hochschild上同调群

The first Hochschild (co)homology when adding arrows to a bound quiver algebra

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.

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

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

具有支撑的Hochschild上同调

Hochschild cohomology with support

本文研究了映射分次Hochschild复形的泛函性质。我们证明了映射分次范畴的范畴MAP自然是一个叠加在具有3-覆盖的Grothendieck拓扑的小范畴上的范畴.对于MAP中的同态上的无穷覆盖的一个相关拓扑，我们证明了取映射分次Hochschild复形定义一个层。从映射分次范畴之间的“注入”的函性出发，得到了“有支撑”的Hochschild复形.我们从这个角度重新凯勒的箭头类别的论点，并介绍和调查一般Grothendieck建设，其中包括映射分级类别与预层的代数和某些广义箭头类别，它们共同构成了一对互补的工具解构Hochschild复形。

关于粘合幂等元下有限维箭图代数的第一Hochschild上同调

On the first Hochschild cohomology of finite dimensional quiver algebras under gluing idempotents

本文研究粘合幂等元得到的箭图代数与原始代数的第一Hochschild上同调李代数结构，证明其或同构或相差一维理想，并给出稳定等价下的新不变量。

Homological invariants of the arrow removal operation

In this paper we show that Gorensteinness, singularity categories and the finite generation condition Fg for the Hochschild cohomology are invariants under the arrow removal operation for a finite dimensional algebra.

关于第一相对Hochschild上同调

On the first relative Hochschild cohomology

本文研究第一相对Hochschild上同调的Lie代数结构，证明在补图简单时其为可解Lie代数，并计算了根方零代数与对偶扩张代数的具体结构。