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Lie Algebras and Lie Groups

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Book cover Lie Algebras and Applications

Part of the book series: Lecture Notes in Physics ((LNP,volume 891))

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Abstract

The relationship between Lie algebras and Lie groups is of great importance. Let the Lie algebra be g and the corresponding Lie group G. The relation is

$$\displaystyle{ \text{Lie algebra}\qquad g \ni X_{i}\mathrm{\ \ }(i = 1,\ldots,r) }$$
(4.1)
$$\displaystyle{ \text{Lie group}\qquad G \ni \exp \left (\sum _{i=1}^{r}\alpha _{ i}X_{i}\right ) }$$
(4.2)

where the α i ’s are the parameters of the group and the sum goes over the order of the group.

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  1. Department of Physics, Yale University, 208120, New Haven, CT, 06520-8120, USA

    Francesco Iachello

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Iachello, F. (2015). Lie Algebras and Lie Groups. In: Lie Algebras and Applications. Lecture Notes in Physics, vol 891. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44494-8_4

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  • DOI: https://doi.org/10.1007/978-3-662-44494-8_4

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