| 吴武顺.关于对偶扩张拟遗传代数的Kazhdan-Lusztig理论[J].数学研究及应用,2009,29(1):146~152 |
| 关于对偶扩张拟遗传代数的Kazhdan-Lusztig理论 |
| On the Kazhdan-Lusztig Theory of Dual Extension Quasi-Hereditary Algebras |
| 投稿时间：2006-12-24 修订日期：2007-09-07 |
| DOI：10.3770/j.issn:1000-341X.2009.01.019 |
| 中文关键词: 拟遗传代数 对偶扩张代数 Kazhdan-Lusztig理论. |
| 英文关键词:quasi-hereditary algebra dual extension algebra Kazhdan-Lusztig theory. |
| 基金项目:漳州师范大学基金(No.SK05012). |
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| 摘要点击次数: 12239 |
| 全文下载次数: 2123 |
| 中文摘要: |
| 为了研究李代数和代数群的表示论, Cline, Parshall与Scott提出了一般拟遗传代数的抽象Kazhdan-Lusztig理论. 本文证明了:若拟遗传代数$B$箭图的点集$Q_0=\{1, \dots, n\}$使得对于任意$i>j$有Hom$_B(P(i), P(j))=0$, 且 $B$ 有相应于长度函数$l$的Kazhdan-Lusztig理论, 则它的对偶扩张代数$A={\cal A}(B)$也有相应于$l$的Kazhdan-Lusztig理论. |
| 英文摘要: |
| 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 $l$. |
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