Using a maximal solvable subalgebra of the Lie algebras gn={sl}(2,R) overrightarrow {oplus}Dn(n+1)L1 we reduce the problem of obtaining the Casimir operators to the integration of only one linear partial differential equation. This reduction allows to prove various results on the admissible degrees of invariants of {g}n, and to construct the quadratic Casimir invariant explicitly for even n. It is moreover shown, that only for 4 values {g}n arises as a non-trivial contraction of Lie algebras. We also point out that the order of a Casimir operator in a fundamental basis of invariants can exceed the dimension of the Lie algebra.
PACS numbers: 02.20.Sv, 02.20.Qs
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