English

Taylor spectrum for modules over Lie algebras

Representation Theory 2021-08-30 v1 Functional Analysis Rings and Algebras

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 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 case of Borel subalgebras of semisimple Lie algebras.

Keywords

Cite

@article{arxiv.2108.12415,
  title  = {Taylor spectrum for modules over Lie algebras},
  author = {Boris Bilich},
  journal= {arXiv preprint arXiv:2108.12415},
  year   = {2021}
}

Comments

11 pages

R2 v1 2026-06-24T05:28:44.312Z