Classification of Curtis-Tits and Phan amalgams with $3$-spherical   diagram
  We classify all non-collapsing Curtis-Tits and Phan amalgams with $3$-spherical diagram over all fields. In particular, we show that amalgams with spherical diagram are unique, a result required by the classification of finite simple groups. We give a simple condition on the amalgam which is necessary and sufficient for it to arise from a group of Kac-Moody type. This also yields a definition of a large class of groups of Kac-Moody type in terms of a finite presentation. 
Rieuwert J. Blok and Corneliu G. Hoffman and Sergey V. Shpectorov
math.GR