González López, ArtemioKamran, NikyOlver, Peter J.2023-06-202023-06-201996-03-151364-503X10.1098/rsta.1996.0044https://hdl.handle.net/20.500.14352/59728© Royal Society of London. Acknowledgment: It is a pleasure to thank the referees for useful comments. Supported in part by DGICYT Grant PB92-0197. Supported in part by an NSERC Grant. Supported in part by NSF Grants DMS 92-04192 and 95-00931.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^2engjournal articlehttp://dx.doi.org/10.1098/rsta.1996.0044http://rsta.royalsocietypublishing.orghttp://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.51.6430&rep=rep1&type=pdfopen access51-732 Complex-variablesQuantal problemsVector-fieldsFísica-Modelos matemáticosFísica matemática