Journal of Lie Theory 31 (2021), No. 1, 093--118
Copyright Heldermann Verlag 2021
Ten-Dimensional Lie Algebras with so(3) Semi-Simple Factor
Narayana M. P. S. K. Bandara
Department of Mathematics and Statistics, University of Toledo, OH 43606, U.S.A.
nbandar2@rockets.utoledo.edu
Gerard Thompson
Department of Mathematics and Statistics, University of Toledo, OH 43606, U.S.A.
gerard.thompson@utoledo.edu
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.
Keywords: Semi-simple factor, radical, nilradical, R-representation, Lie algebra representation.
MSC: 17B05, 17B30, 17B99.
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