Sharp estimnew series of simple Lie algebras of characteristic~3
Sbornik. Mathematics, Tome 76 (1993) no. 2, pp. 389-406
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Three new series of simple finite-dimensional Lie algebras over a field of characteristic 3 are constructed. For explicit realization, these algebras can be represented as a sum of a Lie algebra of general or special Cartan type and of certain of its tensor modules. The algebras have gradings of depth 2 or 4, with a classical zero component; and the author gives a characterization for them in the class of all graded Lie algebras. In order to prove nonisomorphism of these algebras with the Lie algebras of Cartan type, the subalgebras containing a certain invariant set are studied. With a view of systematizing the known examples of simple finite-dimensional Lie algebras of characteristic 3, analogous realizations of two previously known series are also presented.
@article{SM_1993_76_2_a7,
author = {S. M. Skryabin},
title = {Sharp estimnew series of simple {Lie} algebras of characteristic~3},
journal = {Sbornik. Mathematics},
pages = {389--406},
publisher = {mathdoc},
volume = {76},
number = {2},
year = {1993},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1993_76_2_a7/}
}
S. M. Skryabin. Sharp estimnew series of simple Lie algebras of characteristic~3. Sbornik. Mathematics, Tome 76 (1993) no. 2, pp. 389-406. http://geodesic.mathdoc.fr/item/SM_1993_76_2_a7/