Turkowski has classified Lie algebras that have a non-trivial Levi decomposition of dimension up to and including nine. In this work the program is extended to give a partial classification of the corresponding Lie algebras in dimension ten. The key tool is the R-representation, which is the representation of the semi-simple factor by endomorphisms of the radical. The algebras studied here comprise 34 classes that have semi-simple factor so(3) and three exceptions for which semi-simple factor is of dimension six. Most of the algebras have an abelian nilradical, which is probably an artifact of the low dimensions involved. The many remaining cases where the semi-simple factor is sl(2, R) will be investigated in a different venue.
Narayana M. P. S. K. Bandara
1
;
Gerard Thompson
1
1
Department of Mathematics and Statistics, University of Toledo, OH 43606, U.S.A.
Narayana M. P. S. K. Bandara; Gerard Thompson. Ten-Dimensional Lie Algebras with so(3) Semi-Simple Factor. Journal of Lie Theory, Tome 31 (2021) no. 1, pp. 93-118. http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a4/
@article{JOLT_2021_31_1_a4,
author = {Narayana M. P. S. K. Bandara and Gerard Thompson},
title = {Ten-Dimensional {Lie} {Algebras} with so(3) {Semi-Simple} {Factor}},
journal = {Journal of Lie Theory},
pages = {93--118},
year = {2021},
volume = {31},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a4/}
}
TY - JOUR
AU - Narayana M. P. S. K. Bandara
AU - Gerard Thompson
TI - Ten-Dimensional Lie Algebras with so(3) Semi-Simple Factor
JO - Journal of Lie Theory
PY - 2021
SP - 93
EP - 118
VL - 31
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a4/
ID - JOLT_2021_31_1_a4
ER -
%0 Journal Article
%A Narayana M. P. S. K. Bandara
%A Gerard Thompson
%T Ten-Dimensional Lie Algebras with so(3) Semi-Simple Factor
%J Journal of Lie Theory
%D 2021
%P 93-118
%V 31
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a4/
%F JOLT_2021_31_1_a4
