Real Lie Algebras of Differential Operators and Quasi-Exactly Solvable Potentials
Gonzalez-Lopez, Artemio · Kamran, Niky · Olver, Peter J.
Original · EN
We first establish some general results connecting real and complex Lie algebras of first-order differential operators. These are applied to completely classify all finite-dimensional real Lie algebras of first-order differential operators in R². Furthermore, we find all algebras which are quasi-exactly solvable, along with the associated finite-dimensional modules of analytic functions. The resulting real Lie algebras are used to construct new quasi-exactly solvable Schroedinger operators on R².
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