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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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
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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