%0 Journal Article
%A González López, Artemio
%A Kamran, Niky
%A Olver, Peter J.
%T Real Lie algebras of differential operators and quasi-exactly solvable potentials
%D 1996
%@ 1364-503X
%U https://hdl.handle.net/20.500.14352/59728
%X We first establish some general results connecting real and complex Lie algebras ofirst-order diferential operators. These are applied to completely classify all finite-dimensional real Lie algebras of  first-order diferential operators in R^2 . Furthermore, we  find all algebras which are quasi-exactly solvable, along with the associated finitedimensional modules of analytic functions. The resulting real Lie algebras are used to construct new quasi-exactly solvable Schrödinger operators on R^2
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