Abstract
Although it was nearly a century ago that a Norwegian mathematician by the name of Sophus Lie developed his theory of transformation groups, economists have only recently discovered that his group theory can be productively applied to such areas of economic inquiry as the theory of technical change, the theory of duality, dynamic symmetries, economic conservation laws and the theory of invariant index numbers, to name a few (see, e.g., Sato 1981). The main feature of Lie’s work on transformation groups (see Lie 1888–1893 and Lie 1891; Lie and Scheffers 1893) is the study of the relationship between groups and differential equations. A survey of this particular aspect of Lie’s theory is contained in the Appendix to Sato (1981).
This chapter was originally published in The New Palgrave: A Dictionary of Economics, 1st edition, 1987. Edited by John Eatwell, Murray Milgate and Peter Newman
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Bibliography
Lie, S. 1888–93. Theorie der Transformationsgruppen. Ed. F. Engel, 3 vols, Leipzig: Teubner.
Lie, S. 1891. In Vorlesungen über Differentialgleichungen, mit bekannten infinitesimalen Transformationen, ed. G. Scheffers. Leipzig: Teubner.
Lie, S., and G. Scheffers. 1893. Vorlesungen über continuierliche Gruppen mit geometrischen und anderen Anwendungen. Leipzig: Trubner.
Lovelock, D., and H. Ruud. 1975. Tensors, differential forms, and variational principles. New York: Wiley.
Noether, E. 1918. Invariante variationsprobleme. Nachrichten Akademie Wissenschaft Gottingen, Mathematischen-Physischen Kl.II. Trans. M.A. Tavel as ‘Invariant variational problems’, Transport Theory and Statistical Physics 1(3).
Sato, R. 1975. The impact of technical change on the holotheticity of production functions. Paper presented at the World Congress of the Econometric Society, Toronto. Published as Sato (1980).
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Sato, R. 1981. Theory of technical change and economic invariance: Application of Lie Groups. New York: Academic Press.
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Sato, R. (1987). Group (Lie Group) Theory. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95121-5_959-1
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DOI: https://doi.org/10.1057/978-1-349-95121-5_959-1
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Publisher Name: Palgrave Macmillan, London
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