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Izv. Vyssh. Uchebn. Zaved. Mat., 2012, Number 10, Pages 74–78 (Mi ivm8746)  

Brief communications

Finite-dimensional simple Lie algebras with a subalgebra lattice of length 3

A. G. Gein

Chair of Algebra and Discrete Mathematics, Ural Federal University, Ekaterinburg, Russia

Abstract: Lie algebras with a subalgebra lattice of length 2 are well-known. To study a subalgebra lattice of greater length, it is useful to get some information on Lie algebras with a subalgebra lattice of length 3. We show that a finite-dimensional simple Lie algebra over a field of characteristic 0 or a perfect field of prime characteristic greater than 5 whose subalgebra lattice has length 3 may be one of four types.

Keywords: simple Lie algebras, subalgebra lattices, minimal algebras.

Full text: PDF file (142 kB)
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:10, 62–65

Bibliographic databases:

UDC: 512.554
Presented by the member of Editorial Board: Л. Н. Шеврин
Received: 24.02.2012

Citation: A. G. Gein, “Finite-dimensional simple Lie algebras with a subalgebra lattice of length 3”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 10, 74–78; Russian Math. (Iz. VUZ), 56:10 (2012), 62–65

Citation in format AMSBIB
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\by A.~G.~Gein
\paper Finite-dimensional simple Lie algebras with a~subalgebra lattice of length~3
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2012
\issue 10
\pages 74--78
\mathnet{http://mi.mathnet.ru/ivm8746}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3137060}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2012
\vol 56
\issue 10
\pages 62--65
\crossref{https://doi.org/10.3103/S1066369X12100064}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84869425697}


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  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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