Differential algebraic Lie algebras
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- by Phyllis Joan Cassidy PDF
- Trans. Amer. Math. Soc. 247 (1979), 247-273 Request permission
Abstract:
A class of infinite-dimensional Lie algebras over the field $\mathcal {K}$ of constants of a universal differential field $\mathcal {U}$ is studied. The simplest case, defined by homogeneous linear differential equations, is analyzed in detail, and those with underlying set $\mathcal {U} \times \mathcal {U}$ are classified.References
- Pierre Cartier, Groupes formels associés aux anneaux de Witt généralisés, C. R. Acad. Sci. Paris Sér. A-B 265 (1967), A49–A52 (French). MR 218361 —, Modules associés à un groupe formel commutatif. Courbes typiques, C R. Acad. Sci. Paris 265 (1967), 129-132.
- P. J. Cassidy, Differential algebraic groups, Amer. J. Math. 94 (1972), 891–954. MR 360611, DOI 10.2307/2373764 —, Unipotent differential algebraic groups, Contributions to Algebra, A collection of papers dedicated to Ellis Kolchin, Academic Press, New York and London, 1977.
- James E. Humphreys, Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, Vol. 9, Springer-Verlag, New York-Berlin, 1972. MR 0323842, DOI 10.1007/978-1-4612-6398-2
- James E. Humphreys, Linear algebraic groups, Graduate Texts in Mathematics, No. 21, Springer-Verlag, New York-Heidelberg, 1975. MR 0396773, DOI 10.1007/978-1-4684-9443-3
- E. R. Kolchin, Differential algebra and algebraic groups, Pure and Applied Mathematics, Vol. 54, Academic Press, New York-London, 1973. MR 0568864 —, Differential algebraic groups (in preparation); Abstract distributed in conjunction with the Colloquium Lectures delivered at the Seventy-Ninth Summer Meeting of the Amer. Math. Soc., Kalamazoo, Mich., 1975.
- Michel Lazard, Commutative formal groups, Lecture Notes in Mathematics, Vol. 443, Springer-Verlag, Berlin-New York, 1975. MR 0393050, DOI 10.1007/BFb0070554
- Jonathan D. Lubin, Book Review: Commutative formal groups, Bull. Amer. Math. Soc. 82 (1976), no. 4, 535–537. MR 1566880, DOI 10.1090/S0002-9904-1976-14086-4
- J. F. Ritt, Associative differential operations, Ann. of Math. (2) 51 (1950), 756–765. MR 34759, DOI 10.2307/1969379
- J. F. Ritt, Differential groups and formal Lie theory for an infinite number of parameters, Ann. of Math. (2) 52 (1950), 708–726. MR 37308, DOI 10.2307/1969444
- J. F. Ritt, Differential groups of order two, Ann. of Math. (2) 53 (1951), 491–519. MR 40313, DOI 10.2307/1969568
- J. F. Ritt, Subgroups of differential groups, Ann. of Math. (2) 54 (1951), 110–146. MR 43110, DOI 10.2307/1969315
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 247 (1979), 247-273
- MSC: Primary 12H05; Secondary 17B65
- DOI: https://doi.org/10.1090/S0002-9947-1979-0517694-6
- MathSciNet review: 517694