Ten-Dimensional Levi Decomposition Lie Algebras with sl(2, R) Semi-Simple Factor

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 continued and completes the classification of the corresponding Lie algebras in dimension ten, for which the semi -simple factor is sl(2 , R ) . In the approach adopted here, one begins with a nilpotent Lie algebra NR , which will serve as the nilradical of the Levi decomposition algebra S x N that is ultimately constructed. Here N denotes a solvable extension of NR . Two key tools used in obtaining the classification are, the R -representation, that is, the action of sl(2 , R ) as endomorphims of NR and secondly the algebra of R -constants, that is, the subalgebra of N that commutes with the R -representation.