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Lie-algebras of differential-operators in 2 complex-variables

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dc.contributor.authorGonzález López, Artemio
dc.contributor.authorKamran, Niky
dc.contributor.authorOlver, Peter J.
dc.date.accessioned2023-06-20T20:10:06Z
dc.date.available2023-06-20T20:10:06Z
dc.date.issued1992-12
dc.description©Johns Hopkins Univ Press. Research supported in part by an NSERC Grant. Research supported in part by NSF Grant DMS 89-01600.
dc.description.departmentDepto. de Física Teórica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipNSERC
dc.description.sponsorshipNSF
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/32894
dc.identifier.doi10.2307/2374757
dc.identifier.issn0002-9327
dc.identifier.officialurlhttp://dx.doi.org/10.2307/2374757
dc.identifier.relatedurlhttp://www.jstor.org/
dc.identifier.relatedurlhttp://www.math.umn.edu/~olver/q_/lado2.pdf
dc.identifier.urihttps://hdl.handle.net/20.500.14352/59731
dc.issue.number6
dc.journal.titleAmerican journal of mathematics
dc.language.isoeng
dc.page.final1185
dc.page.initial1163
dc.publisherJohns Hopkins Univ Press
dc.relation.projectIDDMS 89-01600
dc.rights.accessRightsopen access
dc.subject.cdu51-73
dc.subject.keywordPhysics
dc.subject.keywordMultidisciplinary
dc.subject.keywordMathematical
dc.subject.ucmFísica-Modelos matemáticos
dc.subject.ucmFísica matemática
dc.titleLie-algebras of differential-operators in 2 complex-variables
dc.typejournal article
dc.volume.number114
dcterms.references[1] M. Abramowitz, and I. Stegun, Handbook of Mathematical Functions, National Bureau of Standards Appl. Math. Series, #55, U.S. Govt. Printing Office, Washington, D.C., 1970. [2] M. Ackerman and R. Hermann, Sophus Lie's 1880 Transformation Group Paper, Math. Sci. Press, Brookline, Mass., 1975. [3] Y. Alhassid, J. Engel, and J. Wu, Algebraic approach to the scattering matrix, Phys. Rev. Lett. 53 (1984), 17-20. [4] V. I. Arnol'd, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer-Verlag, New York, 1983. [5] L. Bianchi, Lezioni sulla Theoria dei Gruppi Continui Finiti di Transformazioni, Enrico Spoerri, Editore, Pisa, 1918. [6] J. E. Campbell, Introductory Treatise on Lie's Theory of Finite Continuous Transformation Groups, The Clarendon Press, Oxford, 1903. [7] É. Cartan, Sur la Structure des Groupes de Transformations Finis et Continus, Thèse, Paris, Nony, 2e edition, Vuibert, 1913, in Oeuvres Completes, Pt. I, v. 1, GauthierVillars, Paris, 1952, 137-287. [8] M. Golubitsky, Primitive actions and maximal subgroups of Lie groups, J. Diff. Geom., 7 (1972), 175-191. [9] A. González-López, N. Kamran, and P. J. Olver, Lie algebras of vector fields in the real plane, Proc. London Math. Soc., (3) 64 (1992), 339-368. [10] N. Jacobson, Lie Algebras, Interscience Publ. Inc., New York, 1962. [11] N. Kamran and P. J. Olver, Equivalence of differential operators, SIAM J. Math. Anal., 20 (1989), 1172-1185. [12] and , Lie algebras of differential operators and Lie-algebraic potentials, J. Math. Anal. Appl., 145 (1990), 342-356. [13] R. D. Levine, Lie algebraic approach to molecular structure and dynamics, in Mathematical Frontiers in Computational Chemical Physics, D. G. Truhlar, ed., IMA Volumes in Mathematics and its Applications, Vol. 15, Springer-Verlag, New York, 1988, 245-2. [14] S. Lie, Theorie der Transformationsgruppen, Math. Ann., 16 (1880), 441-528; also Gesammelte Abhandlungen, vol. 6, B. G. Teubner, Leipzig, 1927, 1-94; see [21 for an English translation. [15] , Theorie der Transformationsgruppen, vol. 3, B. G. Teubner, Leipzig, 1893. [16] Gruppenregister, Gesammelte Abhandlungen, vol. 5, B. G. Teubner, Leipzig, 1924, 767-773. [17] I. G. Macdonald, Symmetric Functions and Hall Polynomials, Clarendon Press, Oxford, 1979. [18] W. Miller, Jr., Lie Theory and Special Functions, Academic Press, New York, 1968. [19] J. Patera, R. T. Sharp, P. Winternitz, and H. Zassenhaus, Invariants of real low dimension Lie algebras, J. Math. Phys., 17 (1976), 986-994. [20] F. Schwarz, A factorization algorithm for linear ordinary differential equations, International Symposium on Symbolic and Algebraic Computation, Proceedings of the ACM-SIGSAM 1989, ACM Press, New York, 1989, 17-25. [21] S. Shnider and P. Winternitz, Nonlinear equations with superposition principles and the theory of transitive primitive Lie algebras, Lett. Math. Phys., 8 (1984), 69-78. [22] A. V. Turbiner, Quasi-exactly solvable problems and sl(2) algebra, Commun. Math. Phys., 118 (1988), 467-474.
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