Projective representations of generalized reduced enveloping algebras

Yi Yang Li; Bin Shu; Yu Feng Yao

doi:10.1016/j.jpaa.2014.07.003

Projective representations of generalized reduced enveloping algebras

Yi Yang Li
, Bin Shu^*
, Yu Feng Yao

^*Corresponding author for this work

School of Mathematical Sciences

Shanghai University of Engineering Science
Shanghai Maritime University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let G be a connected reductive algebraic group over an algebraically closed field of characteristic p>. 0, and g=Lie(G). Let χ∈g* be of standard Levi form. In this paper, we study projective representations of Uχs(g) which is a so-called "higher" reduced enveloping algebra. A reciprocity law on the relation among projective indecomposables, Verma modules and irreducible modules is given. Moreover, a characterization of projective Uχs(g)-modules in terms of filtrations is given.

Original language	English
Pages (from-to)	1645-1656
Number of pages	12
Journal	Journal of Pure and Applied Algebra
Volume	219
Issue number	5
DOIs	https://doi.org/10.1016/j.jpaa.2014.07.003
State	Published - 1 May 2015

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abstract = "Let G be a connected reductive algebraic group over an algebraically closed field of characteristic p>. 0, and g=Lie(G). Let χ∈g* be of standard Levi form. In this paper, we study projective representations of Uχs(g) which is a so-called {"}higher{"} reduced enveloping algebra. A reciprocity law on the relation among projective indecomposables, Verma modules and irreducible modules is given. Moreover, a characterization of projective Uχs(g)-modules in terms of filtrations is given.",

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N2 - Let G be a connected reductive algebraic group over an algebraically closed field of characteristic p>. 0, and g=Lie(G). Let χ∈g* be of standard Levi form. In this paper, we study projective representations of Uχs(g) which is a so-called "higher" reduced enveloping algebra. A reciprocity law on the relation among projective indecomposables, Verma modules and irreducible modules is given. Moreover, a characterization of projective Uχs(g)-modules in terms of filtrations is given.

AB - Let G be a connected reductive algebraic group over an algebraically closed field of characteristic p>. 0, and g=Lie(G). Let χ∈g* be of standard Levi form. In this paper, we study projective representations of Uχs(g) which is a so-called "higher" reduced enveloping algebra. A reciprocity law on the relation among projective indecomposables, Verma modules and irreducible modules is given. Moreover, a characterization of projective Uχs(g)-modules in terms of filtrations is given.

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Projective representations of generalized reduced enveloping algebras

Abstract

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