Hochschild cohomology of truncated basic cycle

Dimensions of the Hochschild cohomology groups of a truncated algebra of a basic cycle are explicitly given. Project supported by the State Education Commission of China, the Chinese Academy of Sciences and the National Natural Science Foundation of China.  

Ringel对偶代数的三角分解

本文证明了树型偏序集的扭双指标代数的Ringel对偶代数存在三角分解，并具体给出了一种三角分解的结构，  

Geometry of the Moment Map for Representations of Quivers

We study the moment map associated to the cotangent bundle of the space of representations of a quiver, determining when it is flat, and giving a stratification of its Marsden–Weinstein reductions. In order to do this we determine the possible dimension vectors of simple representations of deformed preprojective algebras. In an appendix we use deformed preprojective algebras to give a simple proof of much of Kac's Theorem on representations of quivers in characteristic zero.  

Conjugation-uniqueness of exact Borel subalgebras

It is proved that the exact Borel subalgebras of a basic quasi-hereditary algebra are conjugate to each other. Moreover, the inner automorphism group of a basic quasi-hereditary algebra acts transitively on the set of its exact Borel subalgebras. Project supported by the National Natural Science Foundation of China (Grant No. 19771070). and partly supported by the NSF of Hainan Province (Grant No. 19702) and by the Natural Science Foundation of Education Department of Hainan province.  

Locally finite triangulated categories

A k-linear triangulated category is called locally finite provided for any indecomposable object Y in . It has Auslander–Reiten triangles. In this paper, we show that if a (connected) triangulated category has Auslander–Reiten triangles and contains loops, then its Auslander–Reiten quiver is of the form :

Full-size image (<1K)

By using this, we prove that the Auslander–Reiten quiver of any locally finite triangulated category is of the form , where Δ is a Dynkin diagram and G is an automorphism group of . For most automorphism groups G, the triangulated categories with as their Auslander–Reiten quivers are constructed. In particular, a triangulated category with as its Auslander–Reiten quiver is constructed.  

关于项链李代数的结构

Le Bruyn和V．Ginzbrug最近引入了项链李代数。它是定义在箭图上的一种无限堆李代数，在非交换几何研究中起了重要作用。本研究项链李代数结构，证明了当箭图中有长度大于1的循环时，其项链李代数不是幂零李代数，我们还给出了没有圈的箭图上项链李代数的分解。  

Simply connected algebras of polynomial growth

The representation theory of polynomial growth strongly simply connected finite dimensional algebras over an algebraically closed field is established.  

Cyclic and Hochschild homology of 2-nilpotent algebras

We compute the cyclic homology of a 2-nilpotent algebra, using a reduced way of obtaining it for an algebra containing a separable subalgebra as a direct summand.Supported by the Swiss National Foundation, FNSRS.  

图表示范畴的两个子范畴

引进图表示范畴的两个子范畴，研究它们的同调性质。  

Semisimple Representations of Quivers in Characteristic p

We prove that the results of Le Bruyn and Procesi on the varieties parameterizing semisimple representations of quivers hold over an algebraically closed base field of arbitrary characteristic.