Journal of East China Normal University(Natural Science) >

2021 , Vol. 2021 >Issue 3: 17 - 22, 46

DOI: https://doi.org/10.3969/j.issn.1000-5641.2021.03.003

Mathematics

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

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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.

Key words： tilting module; standard Levi form; projective module; nonrestricted representation

Cite this article

Yiyang LI . Tilting modules for the nonrestricted representations of modular Lie algebra[J]. Journal of East China Normal University(Natural Science), 2021 , 2021(3) : 17 -22, 46 . DOI: 10.3969/j.issn.1000-5641.2021.03.003

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