| On the Kazhdan-Lusztig Theory of Dual Extension Quasi-Hereditary Algebras |
| Received:December 24, 2006 Revised:September 07, 2007 |
| Key Words:
quasi-hereditary algebra dual extension algebra Kazhdan-Lusztig theory.
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| Fund Project:the Foundation of Zhangzhou Normal University (No.\, SK05012). |
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| Abstract: |
| 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 $l$. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2009.01.019 |
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