Broué's abelian defect group conjecture for alternating groups

We establish Broué's abelian defect group conjecture for the alternating groups, using the Chuang-Rouquier theorem (proving this for the symmetric groups) and a descent result.

     

The diagram for endomorphism algebras of two-term tilting complexes over self-injective algebras

We construct a diagram between the endomorphism algebra of a two-term projective module complex over a self-injective algebra and the endomorphism algebras of its homology groups and apply the diagram to the tilting theory of self-injective algebras. We give an example of recovering the endomorphism algebra of a two-term tilting complex over a self-injective algebra from the endomorphism algebras of its homology groups with some additional structures which appear in the diagram.     

Derived equivalence of algebras

The derived equivalence and stable equivalence of algebrasR _A ^m and R _B ^m are studied. It is proved, using the tilting complex, thatR _A ^m andR _B ^m are derived-equivalent whenever algebrasA andB are derived-equivalent.     

An型路代数倾斜模的个数

本文证明APR-倾斜过程不改变Dynkin型路代数的倾斜模的个数,并给出计算A_n型路代数的倾斜模的个数的递推公式.     

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．     

Bimodule Complexes via Strong Homotopy Actions

We present a new and explicit method for lifting a tilting complex to a bimodule complex. The key ingredient of our method is the notion of a strong homotopy action in the sense of Stasheff.     

具有性质$(G_k)$的Wakamatsu倾斜模

本文引进了具有性质(Gk)的Wakamatsu倾斜模的概念,并用同调有限子范畴的性质对其进行了刻画．所得结果推广了黄兆泳在文献[1]和[11]中的工作．     

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.