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Carter, MacDonald, Segal
Cambridge University Press eBooks17 Aug 1995
Book chapter
Examples
Carter, MacDonald, Segal · Cambridge University Press eBooks · 1995 · Subscription
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Abstract
A good example of a Lie group is the group E3 of all isometries of euclidean space ℝ3. Euclidean geometry is the study of those properties of subsets of ℝ3 which are preserved when the subset is transformed by an element of E3, so to know what E3 is is the same thing as to know what is meant by Euclidean geometry. In general, Lie groups are the basic tools of geometry.