Abstract
According to Sophus Lie, every local representation of a Lie group G by linear transformations is generated by a representation of the Lie algebra L G of G. The matrices of this representation are linear combinations
, and a neighbourhood of the unity element of G is represented by the matrices
, the x i varying in a neighbourhood of the origin in ℝ n or ℂn. It is true that Lie does not use the modern expressions “exp” and “neighbourhood”, but his statements are equivalent to what I have just said.
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© 1985 Springer-Verlag Berlin Heidelberg
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van der Waerden, B.L. (1985). Representations of Lie Groups and Lie Algebras. In: A History of Algebra. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51599-6_14
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DOI: https://doi.org/10.1007/978-3-642-51599-6_14
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