再论簇倾斜代数的第一Hochschild上同调群

From the potential to the first Hochschild cohomology group of a cluster tilted algebra

The objective of this paper is to give a concrete interpretation of the dimension of the first Hochschild cohomology space of a cyclically oriented or tame cluster tilted algebra in terms of a numerical invariant arising from the potential.

Schurian簇倾斜代数的第一Hochschild上同调群

The first Hochschild cohomology group of a schurian cluster-tilted algebra

给定一个簇倾斜代数B，我们研究它的系数在B-B-双模B中的第一Hochschild上同调群HH ^[1]（B）。我们发现几个后果时，B是代表有限的，也在B是集群倾斜的类型\tilde{\mathbb{A}}的情况下。

有限表示型簇倾斜代数的Hochschild上同调

Hochschild cohomology of the cluster-tilted algebras of finite representation type

计算了有限表示型簇倾斜代数的Hochschild上同调群。

Hochschild上同调与A型M-簇倾斜代数的导类

Hochschild Cohomology and the Derived Class of M-Cluster Tilted Algebras of Type A

我们对所有导出等价于A型m-簇倾斜代数的有限维代数进行了分类。

On the first Hochschild cohomology group of a cluster-tilted algebra

Given a cluster-tilted algebra B, we study its first Hochschild cohomology group HH^1(B) with coefficients in the B-B-bimodule B. If C is a tilted algebra such that B is the relation extension of C, then we show that if C is constrained, or else if B is tame, then HH^1(B) is isomorphic, as a k-vector space, to the direct sum of HH^1(C) with k^{n\_{B,C}}, where n\_{B,C} is an invariant linking the bound quivers of B and C. In the representation-finite case, HH^1(B) can be read off simply by looking at the quiver of B.

Hochschild cohomology of relation extension algebras

Let $B$ be the split extension of a finite dimensional algebra $C$ by a $C$-$C$-bimodule $E$. We define a morphism of associative graded algebras $φ^*:\HH^*(B)\rightarrow \HH^*(C)$ from the Hochschild cohomology of $B$ to that of $C$, extending similar constructions for the first cohomology groups made and studied by Assem, Bustamante, Igusa, Redondo and Schiffler. In the case of a trivial extension $B=C\ltimes E$, we give necessary and sufficient conditions for each $φ^n$ to be surjective. We prove the surjectivity of $φ^1$ for a class of trivial extensions that includes relation extensions a…