Journal of East China Normal University(Natural Science) ›› 2021, Vol. 2021 ›› Issue (3): 17-22, 46.doi: 10.3969/j.issn.1000-5641.2021.03.003

• Mathematics • Previous Articles     Next Articles

Tilting modules for the nonrestricted representations of modular Lie algebra

Yiyang LI()   

  1. School of Mathematics, Physics, and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China
  • Received:2020-01-17 Online:2021-05-25 Published:2021-05-26

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

CLC Number: