Geodesic
Recovering a local Lie group from structure constants
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 1, pp. 98-109

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We construct a coordinate system of the 2nd kind corresponding to canonical coordinates of the 1st kind (in terminology of A. I. Maltsev), thereby obtaining a parametric solution of a Lie system of equations. We also give an integral representation of the group operations $f(x,y)$ of the local Lie group $G$ in canonical coordinates of the 1st kind. Our main tool is the modified formula of A. P. Yuzhakov for implicit mappings. The operation $f(x,y)$ is also represented as a power series, which is the reduced form of the Campbell–Hausdorff series.
Keywords: local Lie group, Campbell–Hausdorff series, formula of A. P. Yuzhakov. 
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     author = {Vitaly A. Stepanenko},
     title = {Recovering a local {Lie} group from structure constants},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {98--109},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2023_16_1_a9/}
}
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Vitaly A. Stepanenko. Recovering a local Lie group from structure constants. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 1, pp. 98-109. http://geodesic.mathdoc.fr/item/JSFU_2023_16_1_a9/