| 关于对偶扩张拟遗传代数的Kazhdan-Lusztig理论 |
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| 引用本文： | 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 |
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| 作者姓名： | 吴武顺 |
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| 作者单位： | 漳州师范学院计算机科学与工程系, 福建 漳州 363000 |
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| 基金项目： | 漳州师范大学基金(No.SK05012). |
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| 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 quasihereditary 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.
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| 关 键 词： | 环论 一般环论 代数 理论 |
| 收稿时间： | 2006-12-24 |
| 修稿时间： | 2007-09-07 |
On the Kazhdan-Lusztig Theory of Dual Extension Quasi-Hereditary Algebras |
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| WU Wu Shun. On the Kazhdan-Lusztig Theory of Dual Extension Quasi-Hereditary Algebras[J]. Journal of Mathematical Research with Applications, 2009, 29(1): 146-152 |
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| Authors: | WU Wu Shun |
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| Affiliation: | Department of Computer Science and Engineering, Zhangzhou Normal University, Fujian 363000, China |
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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 $l$. |
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| Keywords: | quasi-hereditary algebra dual extension algebra Kazhdan-Lusztig theory. |
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