李代数上模的泰勒谱

IF 0.6 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications Pub Date : 2023-01-31 DOI:10.1134/S0016266322030017

B. I. Bilich

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引用次数: 0

摘要

本文将泰勒谱的概念推广到任意李代数上的模，并对有限维模进行了研究。我们证明了在幂零和半单李代数的情况下，谱可以被描述为单子模的集合。我们还证明了这一结果并不适用于可解李代数，并得到了半单李代数的Borel子代数的谱的精确描述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Taylor Spectrum for Modules over Lie Algebras

In this paper we generalize the notion of the Taylor spectrum to modules over an arbitrary Lie algebra and study it for finite-dimensional modules. We show that the spectrum can be described as the set of simple submodules in the case of nilpotent and semisimple Lie algebras. We also show that this result does not hold for solvable Lie algebras and obtain a precise description of the spectrum in the case of Borel subalgebras of semisimple Lie algebras.

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来源期刊

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.