完全温和代数与完全特殊双列代数是 $g$-驯顺的

On Auslander-Reiten components of string complexes for a certain class of symmetric special biserial algebras

Let $\mathbf{k}$ be an algebraically closed field. In this article, inspired by the description of indecomposable objects in the derived category of a gentle algebra obtained by V. Bekkert and H. A. Merklen, we define string complexes for a certain class $\mathscr{C}$ of symmetric special biserial algebras, which are indecomposable perfect complexes in the corresponding derived category. We also prove that if $Λ$ is a $\mathbf{k}$-algebra in the class $\mathscr{C}$ and $P^\bullet$ is a string complex over $Λ$, then $P^\bullet$ lies in the rim of its Auslander-Reiten component.

Representation-tame algebras need not be homologically tame

We show that, also within the class of representation-tame finite dimensional algebras $Λ$, the big left finitistic dimension of $Λ$ may be strictly larger than the little. In fact, the discrepancies $Findim Λ- findim Λ$ need not even be bounded for special biserial algebras which constitute one of the (otherwise) most thoroughly understood classes of tame algebras. More precisely: For every positive integer $r$, we construct a special biserial algebra $Λ$ with the property that $findim Λ= r + 1$, while $Findim Λ= 2r + 1$. In particular, there are infinite dimensional representations of $Λ$ wh…

局部gentle代数的同调条件

Homological conditions on locally gentle algebras

本文研究局部gentle代数的同调性质，通过组合方法描述其中心、素谱和同调维数，并分类其Artin-Schelter Gorenstein、正则及Cohen-Macaulay条件，推广了Stanley定理。

On the Hochschild cohomology of tame Hecke algebras

We explicitly calculate a projective bimodule resolution for a special biserial algebra giving rise to the Hecke algebra H_q(S_4) when q=-1. We then determine the dimensions of the Hochschild cohomology groups.

偏斜-温和代数表示模空间

Moduli of Representations of Skewed-Gentle Algebras

本文证明了偏斜-温和代数（更一般地，宗族代数）的半稳定表示模空间的不可约分支同构于射影空间的乘积，通过将宗族代数表示簇的不可约分支视为偏斜-温和代数的不可约分支并证明其正规性，推广了Carroll-Chindris-Kinser-Weyman关于特殊双列代数表示模空间的类似结果。

Derived tame Nakayama algebras

We determine the derived representation type of Nakayama algebras and prove that a derived tame Nakayama algebra without simple projective module is gentle or derived equivalent to some skewed-gentle algebra, and as a consequence, we determine its singularity category.

周期为四的温顺对称代数

Tame symmetric algebras of period four

本文研究周期为四的温顺对称代数的结构，重点分析 Gabriel 箭图为双序列的情形，给出其箭图必须满足的一系列性质，并证明三角形和正方形自然出现，为后续完整分类奠定基础。

Derived tame quadratic string algebras

In this paper we determine the derived representation type of quadratic string algebras and we prove that every derived tame quadratic string algebra whose quiver has cycles is derived equivalent to some skewed-gentle algebra.

特殊双列代数的模范畴的稳定根

On the stable radical of the module category for special biserial algebras

本文证明了关于特殊双列代数模范畴稳定根的猜想，给出了计算稳定根的算法，并构造了具有任意给定稳定根的 tame 代数。

双列代数与泛型砖模

Biserial algebras and generic bricks

本文利用泛型砖模研究代数闭域上双列代数的砖模无限性，给出显式数值判别条件，并基于极小砖模无限双列代数的完整分类，建立了砖模离散性与τ-倾斜有限性的等价关系。

On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems

In this paper, we investigate properties of the bounded derived category of finite dimensional modules over a gentle or skew-gentle algebra. We show that the Rouquier dimension of the derived category of such an algebra is at most one. Using this result, we prove that the Rouquier dimension of an arbitrary tame projective curve is equal to one, too. Finally, we elaborate the classification of indecomposable objects of the (possibly unbounded) homotopy category of projective modules of a gentle algebra.

Universal deformation rings of modules for generalized Brauer tree algebras of polynomial growth

Let $k$ be an arbitrary field, $Λ$ be a $k$-algebra and $V$ be a $Λ$-module. When it exists, the universal deformation ring $R(Λ,V)$ of $V$ is a $k$-algebra whose local homomorphisms to $R$ parametrize the lifts of $V$ up to $R\otimes_k Λ$, where $R$ is any complete, local commutative Noetherian $k$-algebra with residue field $k$. Symmetric special biserial algebras, which coincide with Brauer graph algebras, can be viewed as generalizing the blocks of finite type $p$-modular group algebras. Bleher and Wackwitz classified the universal deformation rings for all modules for symmetric special bi…

Moduli spaces of modules of Schur-tame algebras

In this paper, we first show that for an acyclic gentle algebra A, the irreducible components of any moduli space of A-modules are products of projective spaces. Next, we show that the nice geometry of the moduli spaces of modules of an algebra does not imply the tameness of the representation type of the algebra in question. Finally, we place these results in the general context of moduli spaces of modules of Schur-tame algebras. More specifically, we show that for an arbitrary Schur-tame algebra A and theta-stable irreducible component C of a module variety of A-modules, the moduli space of …