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Fundam. Prikl. Mat., 2016, Volume 21, Issue 2, Pages 193–216 (Mi fpm1726)  

Uniqueness of addition in Lie algebras of Chevalley type over rings with $1/2$ and $1/3$

A. R. Mayorova

Lomonosov Moscow State University

Abstract: 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 $ė  2$ ($ė  2,3$ in the case of $G_2$).

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English version:
Journal of Mathematical Sciences (New York), 2019, 237:2, 287–303

UDC: 512.554.31

Citation: A. R. Mayorova, “Uniqueness of addition in Lie algebras of Chevalley type over rings with $1/2$ and $1/3$”, Fundam. Prikl. Mat., 21:2 (2016), 193–216; J. Math. Sci., 237:2 (2019), 287–303

Citation in format AMSBIB
\Bibitem{May16}
\by A.~R.~Mayorova
\paper Uniqueness of addition in Lie algebras of Chevalley type over rings with $1/2$ and $1/3$
\jour Fundam. Prikl. Mat.
\yr 2016
\vol 21
\issue 2
\pages 193--216
\mathnet{http://mi.mathnet.ru/fpm1726}
\transl
\jour J. Math. Sci.
\yr 2019
\vol 237
\issue 2
\pages 287--303
\crossref{https://doi.org/10.1007/s10958-019-4156-2}


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