
Journal of Lie Theory 31 (2021), No. 1, 093118 Copyright Heldermann Verlag 2021 TenDimensional Lie Algebras with so(3) SemiSimple 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 nontrivial 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 Rrepresentation, which is the representation of the semisimple factor by endomorphisms of the radical. The algebras studied here comprise 34 classes that have semisimple factor so(3) and three exceptions for which semisimple 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 semisimple factor is sl(2, R) will be investigated in a different venue. Keywords: Semisimple factor, radical, nilradical, Rrepresentation, Lie algebra representation. MSC: 17B05, 17B30, 17B99. [ Fulltextpdf (179 KB)] for subscribers only. 