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Funktsional'nyi Analiz i ego Prilozheniya, 2022, Volume 56, Issue 3, Pages 3–15
DOI: https://doi.org/10.4213/faa4009 (Mi faa4009) 		 
Taylor spectrum for modules over Lie algebras

B. I. Bilichab

a Mathematisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany
b Laboratory on Algebraic Transformation Groups, National Research University "Higher School of Economics", Moscow
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DOI: https://doi.org/10.4213/faa4009
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.
Keywords: Taylor spectrum, Lie algebra cohomology.
Received: 24.04.2022
Revised: 27.05.2022
Accepted: 31.05.2022
English version:
Functional Analysis and Its Applications, 2022, Volume 56, Issue 3, Pages 159–168
DOI: https://doi.org/10.1134/S0016266322030017
Bibliographic databases:
Document Type: Article
UDC: 517.984.22
Language: Russian
Citation: B. I. Bilich, “Taylor spectrum for modules over Lie algebras”, Funktsional. Anal. i Prilozhen., 56:3 (2022), 3–15; Funct. Anal. Appl., 56:3 (2022), 159–168
Citation in format AMSBIB
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\by B.~I.~Bilich
\paper Taylor spectrum for modules over Lie algebras
\jour Funktsional. Anal. i Prilozhen.
\yr 2022
\vol 56
\issue 3
\pages 3--15
\mathnet{http://mi.mathnet.ru/faa4009}
\crossref{https://doi.org/10.4213/faa4009}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4542836}
\transl
\jour Funct. Anal. Appl.
\yr 2022
\vol 56
\issue 3
\pages 159--168
\crossref{https://doi.org/10.1134/S0016266322030017}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85147169298}
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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