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Realizations of real low-dimensional Lie algebras. (English) Zbl 1040.17021
Summary: Using a new powerful technique based on the notion of megaideal, we construct a complete set of inequivalent realizations of real Lie algebras of dimension no greater than four in vector fields on a space of an arbitrary (finite) number of variables. Our classification amends and essentially generalizes earlier works on the subject.
MSC:
17B66Lie algebras of vector fields and related (super)algebras
34M15Algebraic aspects of ODE in the complex domain