The Hochschild cohomology ring modulo nilpotence of a monomial algebra

Support varieties for modules over stacked monomial algebras

In this paper we give necessary and sufficient conditions for the variety of a simple module over a (D,A)-stacked monomial algebra to be nontrivial. This class of algebras was introduced in [Green and Snashall, The Hochschild cohomology ring modulo nilpotence of a stacked monomial algebra, Colloq. Math. 105 (2006), 233-258] and generalizes Koszul and D-Koszul monomial algebras. As a consequence we show that if the variety of every simple module over such an algebra is nontrivial then the algebra is D-Koszul. We give examples of (D,A)-stacked monomial algebras which are not selfinjective but ne…

三角代数的代数版本及P¹×P¹的代数版本与Hochschild上同调

Algebraic versions of $\mathbb{T}^2$ and of $\mathbb{P}^1\times\mathbb{P}^1$ and Hochschild cohomology

本文研究了三角代数及其变形的Hochschild上同调，揭示了其杯积结构与维度变化的非直观特性。

The first cohomology group of the trivial extension of a monomial algebra

Given a finite--dimensional monomial algebra $A$ we consider the trivial extension $TA$ and provide formulae, depending on the characteristic of the field, for the dimensions of the summands $HH_1(A)$ and $\Alt(DA)$ of the first Hochschild cohomology group $HH^1(TA)$. From these a formula for the dimension of $HH^1(TA)$ can be derived.

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。

Maximal tori in $HH^1$ and the fundamental group

We investigate maximal tori in the Hochschild cohomology Lie algebra $HH^1(A)$ of a finite dimensional algebra $A$, and their connection with the fundamental groups associated to presentations of $A$. We prove that every maximal torus in $HH^1(A)$ arises as the dual of some fundamental group of $A$, extending work of Farkas, Green and Marcos; de la Peña and Saorín; and Le Meur. Combining this with known invariance results for Hochschild cohomology, we deduce that (in rough terms) the largest rank of a fundamental group of $A$ is a derived invariant quantity, and among self-injective algebras, …

关于代数的首个$τ$-倾斜Hochschild上同调

On the first $τ$-tilting Hochschild cohomology of an algebra

本文引入了有限维代数的1阶$τ$-Hochschild上同调及其“过剩”概念，证明了零过剩有界箭图代数的2阶Hochschild上同调同构定理，并给出了多种代数的过剩计算公式与$τ$-刚性判据。

受保护的角与韩氏猜想的三分法

Protected corners and a trichotomy for Han's conjecture

研究韩氏猜想，在τ-霍赫希尔德框架下，证明受保护角定理界定生存顶点处的Ext，解决相关扩展猜想，还建立间隙A失败在三个强连通顶点上的三分法，包括排除全无限情形及分类两无限情形为相互哑铃形。