Module Structures on U (ϵ-) for the Euclidean Algebra

Yixin Bao; Yan'an Cai

doi:10.1142/S1005386724000063

Module Structures on U (ϵ^-) for the Euclidean Algebra

Yixin Bao
, Yan'an Cai^*

^*Corresponding author for this work

Harbin Institute of Technology Shenzhen
Soochow University

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

Abstract

We classify modules which are free of rank 1 when restricted to the negative part for the Euclidean Lie algebra. Sufficient and necessary conditions for the simplicity of these modules are given. From these modules we construct modules which are infinitely generated when restricted to the maximal toral subalgebra.

Original language	English
Pages (from-to)	49-56
Number of pages	8
Journal	Algebra Colloquium
Volume	31
Issue number	1
DOIs	https://doi.org/10.1142/S1005386724000063
State	Published - 1 Mar 2024
Externally published	Yes

Keywords

Euclidean algebra
free module
nonweight module
simple module

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10.1142/S1005386724000063

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title = "Module Structures on U (ϵ-) for the Euclidean Algebra",

abstract = "We classify modules which are free of rank 1 when restricted to the negative part for the Euclidean Lie algebra. Sufficient and necessary conditions for the simplicity of these modules are given. From these modules we construct modules which are infinitely generated when restricted to the maximal toral subalgebra.",

keywords = "Euclidean algebra, free module, nonweight module, simple module",

author = "Yixin Bao and Yan'an Cai",

note = "Publisher Copyright: {\textcopyright} 2024 Academy of Mathematics and Systems Science, Chinese Academy of Sciences.",

year = "2024",

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doi = "10.1142/S1005386724000063",

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AU - Cai, Yan'an

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AB - We classify modules which are free of rank 1 when restricted to the negative part for the Euclidean Lie algebra. Sufficient and necessary conditions for the simplicity of these modules are given. From these modules we construct modules which are infinitely generated when restricted to the maximal toral subalgebra.

KW - Euclidean algebra

KW - free module

KW - nonweight module

KW - simple module

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DO - 10.1142/S1005386724000063

M3 - 文章

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Module Structures on U (ϵ^-) for the Euclidean Algebra

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