Abstract
This tutorial does not correspond to an actual oral lecture during the conference at Les Arcs in June, 1980. However, to improve accessibility and understandability of the material in this volume it seemed wise to include a small section on the basic facts and definitions concerning Lie algebras which play a role in control and nonlinear filtering theory. This is what these few pages attempt to do.
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References
A. Bourbaki, Groupes et algèbres de Lie, Chap. 1: Algèbres de Lie, Hermann, 1960.
M. Demazure, Classification des algèbres de Lie filtres, Sèm. Bourbaki 1966/1967, Exp. 326, Benjamin, 1967.
M. Hazewinkel, Tutorial on Manifolds and Vectorfields. This volume.
S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, Acad. Pr., 1978.
J.E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer 1972.
N. Jacobson, Lie Algebras, Dover reprint, 1980.
A.J. Krener, On the Equivalence of Control Systems and the Linearization of nonlinear Systems SIAM J. Control 11(1973), 670–676.
J.P. Serre, Lie Algebras and Lie Groups, Benjamin 1965.
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© 1981 D. Reidel Publishing Company
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Hazewinkel, M. (1981). A Short Tutorial on Lie Algebras. In: Hazewinkel, M., Willems, J.C. (eds) Stochastic Systems: The Mathematics of Filtering and Identification and Applications. NATO Advanced Study Institutes Series, vol 78. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8546-9_6
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DOI: https://doi.org/10.1007/978-94-009-8546-9_6
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