A local-global principle for linear dependence in enveloping algebras of Lie algebras

DOI10.1016/j.laa.2020.03.011zbMath1448.16028arXiv1910.00836OpenAlexW3011130948WikidataQ115344263 ScholiaQ115344263MaRDI QIDQ2309689

Aljaž Zalar, Jakob Cimprič

Publication date: 1 April 2020

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.00836

zbMATH Keywords

Lie algebrauniversal enveloping algebralinear dependenceNullstellensatzlocal linear dependencelocal directional linear dependence

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Universal enveloping (super)algebras (17B35) Simple, semisimple, reductive (super)algebras (17B20) Universal enveloping algebras of Lie algebras (16S30)

Cites Work

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• Local linear dependence of linear partial differential operators
• Some remarks on the center of the universal enveloping algebra of a classical simple Lie algebra
• Unbounded operator algebras and representation theory.
• A local-global principle for linear dependence of noncommutative polynomials.
• On locally linearly dependent operators and derivations
• Prime ideals of the enveloping algebraU(sl₃)
• Lie Groups, Lie Algebras, and Representations
• Introduction to Lie Algebras and Representation Theory

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