Taylor Spectrum for Modules over Lie Algebras

B. I. Bilich

doi:10.1134/S0016266322030017

Taylor Spectrum for Modules over Lie Algebras

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Abstract

Abstract: 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.

Original language	English
Pages (from-to)	159-168
Number of pages	10
Journal	Functional Analysis and its Applications
Volume	56
Issue number	3
DOIs	https://doi.org/10.1134/S0016266322030017
State	Published - Sep 2022
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2022, Pleiades Publishing, Ltd.

Keywords

Lie algebra cohomology
Taylor spectrum

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1134/S0016266322030017

Cite this

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abstract = "Abstract: 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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N2 - Abstract: 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.

AB - Abstract: 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.

KW - Lie algebra cohomology

KW - Taylor spectrum

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DO - 10.1134/S0016266322030017

M3 - Article

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JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

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ER -

Taylor Spectrum for Modules over Lie Algebras

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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