AV modules of finite type on affine space

被引：1

作者：

Billig, Yuly ^{[1
]}

Ingalls, Colin ^{[1
]}

Nasr, Amir ^{[1
]}

机构：

[1] Carleton Univ, Sch Math & Stat, Ottawa, ON, Canada

来源：

JOURNAL OF ALGEBRA | 2023年 / 623卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Lie algebra of vector fields; AV modules; VECTOR-FIELDS; LIE-ALGEBRAS; REPRESENTATIONS;

D O I：

10.1016/j.jalgebra.2023.01.029

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the category of modules admitting compatible actions of the Lie algebra V of vector fields on an affine space and the algebra A of polynomial functions. We show that modules in this category which are finitely generated over A, are free. We also show that this pair of compatible actions is equivalent to commuting actions of the algebra of differential operators and the Lie algebra of vector fields vanishing at the origin. This allows us to construct explicit realizations of such modules as gauge modules.(c) 2023 Elsevier Inc. All rights reserved.

引用

页码：481 / 495

页数：15

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