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Matematicheskie Zametki, 2017, Volume 101, Issue 5, Pages 690–699
DOI: https://doi.org/10.4213/mzm10632 (Mi mzm10632) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Lie Algebras with Abelian Centralizers

V. V. Gorbatsevich

Moscow Aviation Institute (National Research University)
Full-text PDF (426 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm10632
Abstract: In the paper, finite-dimensional real Lie algebras for which the centralizers of all nonzero element are Abelian are studied. These Lie algebras are also characterized by the transitivity condition for the commutation relation for two nonzero elements. A complete description of these Lie algebras up to isomorphism is given. Some results concerning the relationship between the aforementioned Lie algebras and the Lie algebras of vector fields whose orbits are one-dimensional are considered.
Keywords: Lie algebra, centralizer, CT Lie algebra, Lie algebra of vector fields.
Received: 28.11.2014
Revised: 23.09.2016
English version:
Mathematical Notes, 2017, Volume 101, Issue 5, Pages 795–801
DOI: https://doi.org/10.1134/S0001434617050054
Bibliographic databases:
Document Type: Article
UDC: 512.816.3
Language: Russian
Citation: V. V. Gorbatsevich, “Lie Algebras with Abelian Centralizers”, Mat. Zametki, 101:5 (2017), 690–699; Math. Notes, 101:5 (2017), 795–801
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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