Geodesic
Projections of semisimple Lie algebras
Algebra i logika, Tome 58 (2019) no. 2, pp. 149-166

Voir la notice de l'article provenant de la source Math-Net.Ru

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
Mots-clés : modular subalgebra. 
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     author = {A. G. Gein},
     title = {Projections of semisimple {Lie} algebras},
     journal = {Algebra i logika},
     pages = {149--166},
     publisher = {mathdoc},
     volume = {58},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2019_58_2_a0/}
}
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A. G. Gein. Projections of semisimple Lie algebras. Algebra i logika, Tome 58 (2019) no. 2, pp. 149-166. http://geodesic.mathdoc.fr/item/AL_2019_58_2_a0/