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Another representation for the maximal Lie algebra of \(\mathfrak{sl}(n+2,\mathbb R)\) in terms of operators. (English) Zbl 1220.34054

The authors give another short proof for the known fact that the Lie algebra of the second order \(n\)-dimensional vector equation \((y^a)''=0\), \(a=1,2,\ldots ,n\) is isomorphic to \({\mathfrak{s}}{\mathfrak{l}} (n+2,{\mathbb{R}})\).

MSC:

34C14 Symmetries, invariants of ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
22E60 Lie algebras of Lie groups
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