## Differential algebraic Lie algebras

HTML articles powered by AMS MathViewer

- 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**
—, - P. J. Cassidy,
*Differential algebraic groups*, Amer. J. Math.**94**(1972), 891–954. MR**360611**, DOI 10.2307/2373764
—, - 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**
—, - 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

*Modules associés à un groupe formel commutatif. Courbes typiques*, C R. Acad. Sci. Paris

**265**(1967), 129-132.

*Unipotent differential algebraic groups*, Contributions to Algebra, A collection of papers dedicated to Ellis Kolchin, Academic Press, New York and London, 1977.

*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.

## 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