We prove simplicity for incomplete rank 2 Kac-Moody groups over algebraic closures of finite fields with trivial commutation relations between root groups corresponding to prenilpotent pairs.
We don't use the (yet unknown) simplicity of the corresponding finitely generated groups (i.e., when the ground field is finite).
Nevertheless we use the fact that the latter groups are just infinite
Kac-Moody group, twin tree, simplicity, root system, building
20G44 - Kac-Moody groups
20E42 - Groups with a $BN$-pair; buildings [See also 51E24]
51E24 - Buildings and the geometry of diagrams