UNIQUENESS OF ADDITION IN LIE ALGEBRAS OF CHEVALLEY TYPE OVER RINGS WITH 1/2 AND 1/3

摘要

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 ≠ 2 (≠ 2, 3 in the case of G_2).