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Note on Three-Dimensional Lie Groups
Published online by Cambridge University Press: 18 May 2009
Extract
The object of this note is to construct a set of real three-dimensional Lie groups such that every real three-dimensional Lie group is locally isomorphic with some group in the set. The construction is effected by first finding canonical forms for the constants of structure of real three-dimensional Lie algebras; these canonical forms give rise to certain bilinear forms, and the Lie groups are obtained as linear groups isomorphic with groups of automorphisms which leave these bilinear forms invariant.
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- Research Article
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- Copyright © Glasgow Mathematical Journal Trust 1955
References
† See, for example, C. Chevalley, “Theory of Lie groups” (princeton University press), Chapter IV.
‡ The suffixes i, j, k, p, q take the values 1, 2, 3 and the summation convention for repeated indices is used.
§ Chevalley, loc. cit.
∥ |P| denotes the determinant of P, and P' denotes the transpose of P.
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