Dn型路代数倾斜模与AR箭图边缘

代数表示理论是上个世纪七十年代初兴起的代数学的—个新的分支,而倾斜理论是研究代数表示理论的重要工具之一．本文主要对Dn型路代数倾斜模在其对应的AR-箭图上的结构特点进行研究．通过对Dn型路代数A的AR-箭图ΓA分析,证明了：Dn型路代数倾斜模T的—个必要条件是。〈T〉中至少有三个边缘点．     

Dn型路代数本性倾斜模的一个必要条件

倾斜理论是研究代数表示理论的重要工具之一．本文主要对Dn（n≥4），E6，E7，E8型路代数倾斜模在其对应的AR-箭图上的结构持点进行研究．通过对Dn（n≥4），上E6，E7，E8型路代数A的AR-箭图ΓA分析证明了Dn≥4），E6，E7，E8型路代数本性慨斜模TA的一个必要条件是：在A的AR-箭图ΓA的每个边缘的r-轨道都有TA的不可分解直和项对应的点．     

投射直向表示代数

本文给出了有限维结合代数上 last 投射模直向的判别.并讨论了任一不可分解投射模都直向的代数的 AR-箭图上模的直向性.     

投射直向表示代数

本文给出了有限维结合代数上last投射模直向的判别。并讨论了任一不可分解投射模都直向的代数的AR-箭图上模的直向性。     

AR-箭图的构造和矩阵双模问题

本文简要介绍了Artin代数表示理论中的下述内容:Auslander-Reiten箭图(简称AR-箭图)稳定分支的结构,野型遗传代数稳定分支的性质,代数闭域上有限维代数Λ引出的矩阵双模问题、对偶的余双模问题及其相伴的具有余代数结构的双模(简称box), modΛ、P_1(Λ)及相伴box的表示范畴之间几乎可列序列的几乎一一对应,驯顺代数Λ上任意两个模之间态射集的维数和性质;最后介绍了代数的驯顺性与其模范畴的齐性.     

关于平移箭图上的截点圈

在本文中,我们证明了在一定条件下平移箭图中不存在截点圈(sectional cycle),从而推广了在阿丁代数的AR-箭图上Bautista和Smalφ的相应结果。     

m-重代数A~((m))上的倾斜模

设A是代数闭域k上的有限维遗传代数,A~((m))和ζ_m(A)分别是A的m-重代数和m-丛范畴.众所周知,代数A~((m))的投射维数不超过m的基本的(basic)倾斜模与m-丛范畴ζ_m(A)的基本的倾斜对象一一对应,这是本文进一步研究m-重代数的倾斜模的原因.本文综述m-重代数A~((m))的偏倾斜模的补、倾斜箭图、倾斜模的自同态代数以及生成子-余生成子的自同态代数的整体维数的值分布.     

倾斜代数的AR序列的结构

Ringel和Happe[3]给出了倾斜代数的连结序列。本文给出了落入H（AT）和落入Y（AT）的AR序列的结构；同时得到倾斜代数的以不可分投射模为终点的汇射和以不可分内射模为起点的源射的形式。这些连同序列确定了倾斜代数的AR箭图，而可以直接由相应的遗传代数的AR箭图得出。     

对应于tame遗传代数的bocses(Ⅱ)

展示了tame遗传代数的bocses.对于每个维数d,给出了对应的仅含有不可约映射的极小bocses.除了有限个点外,这些极小bocses与对应代数的AR-箭图中具有性质dim(topM)<d的不可分解模M组成的满子图完全重合.     

倾斜模与recollement的比较函子

本文目的是提供一个由BB-倾斜模确定的TTF-理论,并由此考察由BB-倾斜模诱导的recollement和单边recollement的比较函子.     

$T_{2}(T)$的几乎可裂序列及几乎$\mathcal {D}$-可裂序列

The AR-quiver and derived equivalence are two important subjects in the representation theory of finite dimensional algebras, and for them there are two important research tools-AR-sequences and D-split sequences. So in order to study the representations of triangular matrix algebra T2 (T ) = T0TT where T is a finite dimensional algebra over a field, it is important to determine its AR-sequences and D-split sequences. The aim of this paper is to construct the right(left) almost split morphisms, irreducible morphisms, almost split sequences and D-split sequences of T2 (T) through the corresponding morphisms and sequences of T. Some interesting results are obtained.     

Comparisons of recollements and tilting modules

The purpose of this paper is to provide the TTF-theories and investigate the comparisons of recollements(one-sided recollements) both induced by the BB-tilting modules.     

Characterizations of algebras with small homological dimensions

We introduce the class of double tilted algebras, containing the class of tilted algebras and prove various characterizations. In particular, we show that the class of double tilted algebras is the class of all artin algebras whose AR-quiver admits a faithful double section with a natural property. Moreover, we prove that the class of double tilted algebras coincides with the class of all artin algebras of global dimension three, for which every indecomposable finitely generated module has projective or injective dimension at most one. We also describe the structure of the category of finitely generated modules as well as the AR-quiver of double tilted algebras.     

Folding derived categories with Frobenius functors

Following the work [B. Deng, J. Du, Frobenius morphisms and representations of algebras, Trans. Amer. Math. Soc. 358 (2006) 3591-3622], we show that a Frobenius morphism F on an algebra A induces naturally a functor F on the (bounded) derived category D^b(A) of , and we further prove that the derived category D^b(A^F) of for the F-fixed point algebra A^F is naturally embedded as the triangulated subcategory D^b(A)^F of F-stable objects in D^b(A). When applying the theory to an algebra with finite global dimension, we discover a folding relation between the Auslander-Reiten triangles in D^b(A^F) and those in D^b(A). Thus, the AR-quiver of D^b(A^F) can be obtained by folding the AR-quiver of D^b(A). Finally, we further extend this relation to the root categories ?(A^F) of A^F and ?(A) of A, and show that, when A is hereditary, this folding relation over the indecomposable objects in ?(A^F) and ?(A) results in the same relation on the associated root systems as induced from the graph folding relation.     

The center of an effect algebra

An effect algebra is a partial algebra modeled on the standard effect algebra of positive self-adjoint operators dominated by the identity on a Hilbert space. Every effect algebra is partially ordered in a natural way, as suggested by the partial order on the standard effect algebra. An effect algebra is said to be distributive if, as a poset, it forms a distributive lattice. We define and study the center of an effect algebra, relate it to cartesian-product factorizations, determine the center of the standard effect algebra, and characterize all finite distributive effect algebras as products of chains and diamonds.     

Hammocks and the Nazarova-Roiter Algorithm

Hammocks have been considered by Brenner [1], who gave a numericalcriterion for a finite translation quiver to be the Auslander–Reitenquiver of some representation-finite algebra. Ringel and Vossieck[11] gave a combinatorial definition of left hammocks whichgeneralised the concept of hammocks in the sense of Brenner,as a translation quiver H and an additive function h on H (calledthe hammock function) satisfying some conditions. They showedthat a thin left hammock with finitely many projective verticesis just the preprojective component of the Auslander–Reitenquiver of the category of S-spaces, where S is a finite partiallyordered set (abbreviated as ‘poset’). An importantrole in the representation theory of posets is played by twodifferentiation algorithms. One of the algorithms was developedby Nazarova and Roiter [8], and it reduces a poset S with amaximal element a to a new poset S'=_aS. The second algorithmwas developed by Zavadskij [13], and it reduces a poset S witha suitable pair (a, b) of elements a, b to a new poset S'=_(a,b)S.The main purpose of this paper is to construct new left hammocksfrom a given one, and to show the relationship between thesenew left hammocks and the Nazarova–Roiter algorithm. Ina later paper [5], we discuss the relationship between hammocksand the Zavadskij algorithm.     

Coorbits of Quantum Homogeneous Spaces

The notion of coorbits for spaces with quantum group actions is introduced. A space with a quantum group action is given by a pair of algebras: an associative algebra which is the analog of a classical topological space, and a Hopf algebra which is the analog of a classical topological group. The Hopf algebra acts on the associative algebra via a comodule structure mapping which is also an algebra homomorphism. For a space with a quantum group action, a coorbit is a pair of spaces given by the image and the kernel of an algebra homomorphism from the associative algebra to the Hopf algebra. The coorbits of several types of quantum homogeneous spaces are discussed. In the case when the associative algebra is the group algebra of a group and the Hopf algebra is a quotient of the group algebra, the connection between the set of coorbits and the character group is established.