Abstract
The concept of a group was described briefly in Chapter 1. This chapter serves as an introduction to a special class of groups, the Lie groups, which are named after Norwegian mathematician Sophus Lie.1 Furthermore, when referring to Lie groups, what will be meant in the context of this book is matrix Lie groups, where each element of the group is a square invertible matrix. Other books focusing specifically on matrix groups include [3, 9, 19].
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References
Angeles, J., Rational Kinematics, Springer, New York, 1989.
Artin, M., Algebra, Prentice Hall, Upper Saddle River, NJ, 1991.
Baker, A., Matrix Groups: An Introduction to Lie Group Theory, Springer, New York, 2002.
Baker, H.F., “Alternants and continuous groups,” Proc. London Math. Soc. (Second Series),3, pp. 24–47, 1904.
Birkhoff, G., MacLane, S., A Survey of Modern Algebra, 4th ed., Macmillan Publishing Co., New York, 1977.
Bottema, O., Roth, B., Theoretical Kinematics, Dover, New York, 1990.
Campbell, J.E., “On a law of combination of operators,” Proc. London Math. Soc., 29, pp. 14–32, 1897.
Chirikjian, G.S., Kyatkin, A.B., Engineering Applications of Noncommutative Harmonic Analysis, CRC Press, Boca Raton, FL, 2001.
Curtis, M.L., Matrix Groups, 2nd ed., Springer, New York, 1984.
Gilmore, R., Lie Groups, Lie Algebras, and Some of Their Applications, Dover, New York, 2006.
Hausdorff, F., “Die symbolische Exponentialformel in der Gruppentheorie,” Berich. der Sachsichen Akad. Wissensch., 58, pp. 19–48, 1906.
Inui, T., Tanabe, Y., Onodera, Y., Group Theory and Its Applications in Physics, 2nd ed., Springer-Verlag, New York, 1996.
Kol´aˇr, I.,Michor, P.W., Slov´ak, J., Natural Operations in Differential Geometry, Springer- Verlag, Berlin, 1993.
McCarthy, J.M., An Introduction to Theoretical Kinematics, MIT Press, Cambridge, MA, 1990.
Miller, W., Jr., Symmetry Groups and Their Applications, Academic Press, New York, 1972.
Murray, R.M., Li, Z., Sastry, S.S., A Mathematical Introduction to Robotic Manipulation, CRC Press, Boca Raton, FL, 1994.
Park, F.C., The Optimal Kinematic Design of Mechanisms, Ph.D. thesis, Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 1991.
Selig, J.M., Geometrical Methods in Robotics, 2nd ed., Springer, New York, 2005.
Tapp, K., Matrix Groups for Undergraduates, American Mathematical Society, Providence, RI, 2005.
Varadarajan, V.S., Lie Groups, Lie Algebras, and their Representations, Springer-Verlag, New York, 1984.
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Chirikjian, G.S. (2012). Lie Groups I: Introduction and Examples. In: Stochastic Models, Information Theory, and Lie Groups, Volume 2. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4944-9_1
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DOI: https://doi.org/10.1007/978-0-8176-4944-9_1
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