Geodesic
Uniqueness of addition in Lie algebras of Chevalley type over rings with $1/2$ and $1/3$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 2, pp. 193-216

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In this paper, it is proved that Lie algebras of Chevalley type ($A_n$, $B_n$, $C_n$, $D_n$, $E_6$, $E_7$, $E_8$, $F_4$, and $G_2$) over associative commutative rings with $1/2$ (with $1/2$ and $1/3$ in the case of $G_2$) have unique addition. As a corollary of this theorem, we note the uniqueness of addition in semisimple Lie algebras of Chevalley type over fields of characteristic ${\ne}\, 2$ (${\ne}\, 2,3$ in the case of $G_2$). 
@article{FPM_2016_21_2_a8,
     author = {A. R. Mayorova},
     title = {Uniqueness of addition in {Lie} algebras of {Chevalley} type over rings with $1/2$ and $1/3$},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {193--216},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2016_21_2_a8/}
}
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A. R. Mayorova. Uniqueness of addition in Lie algebras of Chevalley type over rings with $1/2$ and $1/3$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 2, pp. 193-216. http://geodesic.mathdoc.fr/item/FPM_2016_21_2_a8/