量子环面上的导子李代数模的导子

J4 ›› 2013, Vol. 48 ›› Issue (6): 46-50.

量子环面上的导子李代数模的导子

姜景连

武夷学院数学与计算机系, 福建武夷山 354300

收稿日期:2012-11-20 出版日期:2013-06-20 发布日期:2013-06-09
作者简介:姜景连(1967- ),女,硕士,副教授,研究方向为代数学. Email:jljiang6708@yahoo.com.cn
基金资助:
福建省教育厅A类科技项目(JA12330)

The derivations from the Lie algebra of derivations for quantum torus to its modules

JIANG Jing-lian

Department of Mathematics and Computer, Wuyi University, Wuyishan 354300, Fujian, China

Received:2012-11-20 Online:2013-06-20 Published:2013-06-09

摘要/Abstract

摘要：

设q是p次本原单位根,L是两个变量的量子环面Cq上的导子李代数, W=Fαg (V)是由函子Fαg 作用在有限维gl2-模V上诱导的L-模。那么李代数L到其模W的导子除几种情形外都是内导子,且由此1-上同调群H1(L, W)在大多数情形下是平凡的。

关键词: 量子环面李代数;模;本原单位根;导子

Abstract:

Let q be a pth root of unity, and L be the derivation Lie algebra over the rank two quantum torus Cq. Let W=Fαg (V) be the L-module define by functor Fαg applied to a finite dimensional gl2-module V. Then the derivations from L to its modules W are most often inner, except for some case, and the first cohomology group H1(L, W) is most often trivial.

Key words: Lie algebra over the quantum torus; module; root of unity; derivation

姜景连. 量子环面上的导子李代数模的导子[J]. J4, 2013, 48(6): 46-50.

JIANG Jing-lian. The derivations from the Lie algebra of derivations for quantum torus to its modules[J]. J4, 2013, 48(6): 46-50.

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