On the Kazhdan-Lusztig Theory of Dual Extension Quasi-Hereditary Algebras
Received:December 24, 2006  Revised:September 07, 2007
Key Word: quasi-hereditary algebra   dual extension algebra   Kazhdan-Lusztig theory.
Fund ProjectL:the Foundation of Zhangzhou Normal University (No.\, SK05012).
 Author Name Affiliation WU Wu Shun Department of Computer Science and Engineering, Zhangzhou Normal University, Fujian 363000, China
Hits: 11794
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 $Q_0=\{1, \ldots, n\}$ such that Hom$_B(P(i), P(j))=0$ 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 $A={\cal A}(B)$ has also the Kazhdan-Lusztig theory relative to the length function $l$.