On the Kazhdan-Lusztig Theory of Dual Extension Quasi-Hereditary Algebras

In order to study the representation theory of Lie algebras and algebraic groups,Cline,Parshall and Scott put forward the notion of abstract Kazhdan-Lusztig theory for quasi-hereditary algebras.Assume that a quasi-hereditary algebra B has the vertex set Q0 = {1,...,n} such that HomB(P(i),P(j)) = 0 for i > j.In this paper,it is shown that if the quasi-hereditary algebra B has a Kazhdan-Lusztig theory relative to a length function l,then its dual extension algebra A = A(B) has also the Kazhdan-Lusztig theory relative to the length function l.

RCC11复合表的表示(英文)

主要研究熟知的区域连接演算(region connection calculus,简称RCC)的关系代数方面的性质.证明了补闭圆盘代数恰好构成RCC11复合表的一个表示,其中,RCC11复合表是由Düntsch于1999年引入的.补闭圆盘代数由两类区域构成:一类是实平面中的所有闭圆盘;另一类是实平面中的所有闭圆盘的补的闭包组成.而连接关系为经典的Whiteheadean连接,即对区域a,b,aCb(表示a,b有连接关系)当且仅当a∩b≠ф.