Gauge Modules for the Lie Algebras of Vector Fields on Affine Varieties

被引：0
作者：
Yuly Billig
Jonathan Nilsson
André Zaidan
机构：
[1] Carleton University,School of Mathematics and Statistics
[2] Chalmers University of Technology,Mathematical Sciences
[3] Universidade de São Paulo,Instituto de Matemática e Estatística
来源：
Algebras and Representation Theory | 2021年 / 24卷
关键词：
Simple modules; Lie algebra of vector fields; Primary 17B20; 17B66; Secondary 13N15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
For a smooth irreducible affine algebraic variety we study a class of gauge modules admitting compatible actions of both the algebra A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {A}$\end{document} of functions and the Lie algebra V\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {V}$\end{document} of vector fields on the variety. We prove that a gauge module corresponding to a simple glN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathfrak {gl}_{N}$\end{document}-module is irreducible as a module over the Lie algebra of vector fields unless it appears in the de Rham complex.
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页码：1141 / 1153
页数：12
相关论文
共 14 条
[1]  
Bavula VV(1992)Generalized Weyl algebras and their representations Algebra i Analiz 4 75-97
[2]  
Bavula VV(2010)Generators and defining relations for the ring of differential operators on a smooth affine algebraic variety Algebras and Representation Theory 13 159-187
[3]  
Billig Y(2007)Jet modules, Canad J. Math 59 712-729
[4]  
Billig Y(2018)Lie algebras of vector fields on smooth affine varieties Commun. Algebra 46 3413-3429
[5]  
Futorny V(2019)Representations of the Lie algebra of vector fields on affine varieties Israel J. of Math. 233 379-399
[6]  
Billig Y(2019)Representations of the Lie algebra of vector fields on a sphere J. Pure and Appl. Algebra 223 3581-3593
[7]  
Futorny V(1981)The irreducible representations of the Lie algebra Adv. Math. 39 69-110
[8]  
Nilsson J(1996)(2) and of the Weyl algebra J. Algebra 182 401-421
[9]  
Billig Y(1986)Irreducible representations of the Lie-algebra of the diffeomorphisms of a J. London Math. Soc. 33 33-39
[10]  
Nilsson J(2000)-dimensional torus J. Algebra 228 580-585
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