Uniqueness of Addition in Lie Algebras of Chevalley Type over Rings with 1/2 and 1/3
- 5 Downloads
In this paper, it is proved that Lie algebras of Chevalley type (An, Bn, Cn, Dn, 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).
Unable to display preview. Download preview PDF.
- 1.I. V. Arzhantsev, “Uniqueness of addition in Lie algebra sl(2),” in: Fong Yuen, A. A. Mikhalev, and E. Zelmanov, eds., Lie Algebras, Rings and Related Topics, Springer (2000), pp. 1–4.Google Scholar
- 3.I. V. Arzhantsev, “Some results on uniqueness of addition in Lie algebras,” in: I. Bajo and E. Sanmartín, eds., Proc. of the First Colloquium on Lie Theory and Applications, Univ. de Vigo (2002), pp. 19–24.Google Scholar
- 4.N. Bourbaki, Elements of Mathematics. Lie Groups and Lie Algebras, Springer (1998).Google Scholar