Publication: Lie-algebras of differential-operators in 2 complex-variables
Loading...
Official URL
Full text at PDC
Publication Date
1992-12
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Johns Hopkins Univ Press
Citations
Exportar
Abstract
Description
©Johns Hopkins Univ Press.
Research supported in part by an NSERC Grant.
Research supported in part by NSF Grant DMS 89-01600.
UCM subjects
Unesco subjects
Keywords
Citation
[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.