数学

模李代数非限制表示中的倾斜模

  • 李宜阳
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  • 上海工程技术大学 数理与统计学院, 上海 201620
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

收稿日期: 2020-01-17

  网络出版日期: 2021-05-26

基金资助

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)

Tilting modules for the nonrestricted representations of modular Lie algebra

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

Received date: 2020-01-17

  Online published: 2021-05-26

摘要

$ 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}}) $ $ {\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.

本文引用格式

李宜阳 . 模李代数非限制表示中的倾斜模[J]. 华东师范大学学报(自然科学版), 2021 , 2021(3) : 17 -22, 46 . DOI: 10.3969/j.issn.1000-5641.2021.03.003

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.

参考文献

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