模李代数非限制表示中的倾斜模

李宜阳

doi:10.3969/j.issn.1000-5641.2021.03.003

模李代数非限制表示中的倾斜模

doi: 10.3969/j.issn.1000-5641.2021.03.003

李宜阳

上海工程技术大学数理与统计学院, 上海　201620

基金项目: 国家自然科学基金(11771279, 11671138); 新疆维吾尔自治区自然科学基金(2016D01A014)

详细信息

作者简介:
李宜阳, 男, 博士, 副教授, 研究方向为李代数和表示理论. E-mail: liyiyang1979@outlook.com

中图分类号: O152, O154.2
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- 被引次数: 0
出版历程
- 收稿日期: 2020-01-17
- 刊出日期: 2021-05-01

Tilting modules for the nonrestricted representations of modular Lie algebra

LI Yiyang

School of Mathematics, Physics, and Statistics, Shanghai University of Engineering Science, Shanghai　201620, China

摘要

摘要: 令$ G $为素特征$ p $的代数闭域$ k $上连通的简约代数群. 李代数$ {\frak {g}} = {\rm{Lie}}(G) $, $ U_{\chi}({\frak {g}}) $是$ {\frak {g}} $的约化包络代数. 在$ p $-特征$ \chi $具有标准 Levi 型时, 证明了一个$ U_{\chi}({\frak {g}}) $-模$ Q $是倾斜模的充分必要条件是$ Q $是投射模.
- 倾斜模 /
- 标准 Levi 型 /
- 投射模 /
- 非限制表示
Abstract: Let $ G $ be a connected reductive algebraic group over an algebraically closed field $ k $ of prime characteristic $ p $, and let$ {\frak {g}} = {\rm{Lie}}(G) $, $U_{\chi}({\frak {g}}) $ be the reduced enveloping algebra. In this paper, when $ p $-character $ \chi $ has the standard Levi form, we prove that a $ U_{\chi}({\frak {g}}) $-module $ Q $ is a tilting module if and only if it is projective.
- tilting module /
- standard Levi form /
- projective module /
- nonrestricted representation

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Fig. 1 Commutative diagram

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参考文献(12)

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