Geodesic
Taylor spectrum for modules over Lie algebras
Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 3, pp. 3-15

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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. 
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     author = {B. I. Bilich},
     title = {Taylor spectrum for modules over {Lie} algebras},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {3--15},
     publisher = {mathdoc},
     volume = {56},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2022_56_3_a0/}
}
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B. I. Bilich. Taylor spectrum for modules over Lie algebras. Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 3, pp. 3-15. http://geodesic.mathdoc.fr/item/FAA_2022_56_3_a0/