The cohomology of the full directed graph complex

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。

关于奇数p-群的第一Hochschild上同调的可解性

On solvability of the first Hochschild cohomology of odd p-groups

本文研究了奇数p-群的第一Hochschild上同调作为李代数的可解性条件，通过构造有向图来确定其结构特性。

$BV$-structure on Hochschild cohomology for exceptional local algebras of quaternion type. Case of the small parameter

This is the second paper in the cycle of articles about $BV$-structure on Hochshild cohomology of exceptional algebras of quaternion type. We give $BV$-structure's full description in the case of quaternion algebras $R(k,0,d)$, defined by parameter $k = 2$ according to Erdmann classification.

A Hochschild Cohomology Comparison Theorem for prestacks

We generalize and clarify Gerstenhaber and Schack's "Special Cohomology Comparison Theorem". More specifically we obtain a fully faithful functor between the derived categories of bimodules over a prestack over a small category U and the derived category of bimodules over its corresponding fibered category. In contrast to Gerstenhaber and Schack we do not have to assume that U is a poset.

Descent cohomology and factorizations of groups

The aim of the paper is to give a full classification of factorizations of groups in terms of descent cohomology (pointed) sets introduced in [5]. We show that descent cohomology includes Serre's non-abelian group cohomology as a special case. This enables us to generalize Serre's theory further to include monoids.

Comparison morphisms and the Hochschild cohomology ring of truncated quiver algebras

A main contribution of this paper is the explicit construction of comparison morphisms between the standard bar resolution and Bardzell's minimal resolution for truncated quiver algebras (TQA's). As a direct application we describe explicitely the Yoneda product and derive several results on the structure of the cohomology ring of TQA's. For instance, we show that the product of odd degree cohomology classes is always zero. We prove that TQA's associated with quivers with no cycles or with neither sinks nor sources have trivial cohomology rings. On the other side we exhibit a fundamental examp…