Global dimensions of endomorphism algebras for generator-cogenerators over $m$-replicated algebras

关于极小生成-余生成子的整体维数为三的自同态代数

On the global dimension three endomorphism algebras of the minimal generator-cogenerator

本文研究极小生成-余生成子自同态环整体维数为三的代数（表示遗传代数），证明其无挠有限性及特定条件下的同调性质，并给出其属于特定倾斜代数类的充分条件。

Rigidity degrees of indecomposable modules over representation-finite self-injective algebras

The rigidity degree of a generator-cogenerator determines the dominant dimension of its endomorphism algebra, and is closely related to a recently introduced homological dimension -- rigidity dimension. In this paper, we give explicit formulae for the rigidity degrees of all indecomposable modules over representation-finite self-injective algebras by developing combinatorial methods from the Euclidean algorithm. As an application, the rigidity dimensions of some algebras of types $A$ and $E$ are given.

更高阶森田-立川对应

Higher Morita-Tachikawa correspondence

本文通过引入拟生成元和拟上生成元的概念，推广生成元和上生成元，提出考虑相对支配维数的更高阶森田-立川对应，且该对应在特定诺特代数上成立。

关于箭图格拉斯曼流形与gen-有限模的轨道闭包

On quiver Grassmannians and orbit closures for gen-finite modules

本文通过典范倾斜模与再收集构造gen-有限模的轨道闭包及箭图格拉斯曼流形的去奇异化，推广了2017年相关结果，并给出对偶版本以处理cogen-有限模。

Auslander-Gorenstein algebras from Serre-formal algebras via replication

We introduce a new family of algebras, called Serre-formal algebras. They are Iwanaga-Gorenstein algebras for which applying any power of the Serre functor on any indecomposable projective module, the result remains a stalk complex. Typical examples are given by (higher) hereditary algebras and self-injective algebras; it turns out that other interesting algebras such as (higher) canonical algebras are also Serre-formal. Starting from a Serre-formal algebra, we consider a series of algebras - called the replicated algebras - given by certain subquotients of its repetitive algebra. We calculate…

论诺特代数、舒尔函子与Hemmer-Nakano维数

On Noetherian algebras, Schur functors and Hemmer-Nakano dimensions

本文研究（投射）诺特代数B的模范畴与B上生成-相对上生成子的自同态代数的模范畴间联系的质量，通过舒尔函子分析Hemmer-Nakano维数，建立整数情形与有限维情形的计算关联，推导舒尔代数和BGG范畴O的结果并展示形变的结构性质。