Uniqueness of Addition in Lie Algebras of Chevalley Type over Rings with 1/2 and 1/3

Resumo

In this paper, it is proved that Lie algebras of Chevalley type (A_n, B_n, C_n, D_n, E₆, E₇, E₈, F₄, and G₂) over associative commutative rings with 1/2 (with 1/2 and 1/3 in the case of G₂) 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 ≠ 2 (≠ 2, 3 in the case of G₂).