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Algebra i logika, 2019, Volume 58, Number 2, Pages 149–166
DOI: https://doi.org/10.33048/alglog.2019.58.201 (Mi al887) 		 
Projections of semisimple Lie algebras

A. G. Gein

Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
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DOI: https://doi.org/10.33048/alglog.2019.58.201
Abstract: It is proved that the property of being a semisimple algebra is preserved under projections (lattice isomorphisms) for locally finite-dimensional Lie algebras over a perfect field of characteristic not equal to 2 and 3, except for the projection of a three-dimensional simple nonsplit algebra. Over fields with the same restrictions, we give a lattice characterization of a three-dimensional simple split Lie algebra and a direct product of a one-dimensional algebra and a three-dimensional simple nonsplit one.
Keywords: subalgebra lattice, lattice isomorphism, semisimple Lie algebras, modular subalgebra.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 02.A03.21.0006
Supported through the Competitiveness Project (Agreement No. 02.A03.21.0006 of 27.08.2013 between the Ministry of Education and Science of the Russian Federation and the Ural Federal University).
Received: 27.01.2018
Revised: 09.07.2019
English version:
Algebra and Logic, 2019, Volume 58, Issue 2, Pages 103–114
DOI: https://doi.org/10.1007/s10469-019-09529-z
Bibliographic databases:
Document Type: Article
UDC: 512.565
Language: Russian
Citation: A. G. Gein, “Projections of semisimple Lie algebras”, Algebra Logika, 58:2 (2019), 149–166; Algebra and Logic, 58:2 (2019), 103–114
Citation in format AMSBIB
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