Taylor spectrum for modules over Lie algebras. (English. Russian original) Zbl 1529.17033
Funct. Anal. Appl. 56, No. 3, 159-168 (2022); translation from Funkts. Anal. Prilozh. 56, No. 3, 3-15 (2022).
Summary: 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.
MSC:
| 17B56 | Cohomology of Lie (super)algebras |
| 47A13 | Several-variable operator theory (spectral, Fredholm, etc.) |
Software:
MathOverflowReferences:
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