
Journal of Lie Theory 16 (2006), No. 1, 001018 Copyright Heldermann Verlag 2006 Defining Amalgams of Compact Lie Groups Ralf Gramlich Fachbereich Mathematik, Technische Universität, Schlossgartenstr. 7, 64289 Darmstadt, Germany gramlich@mathematik.tudarmstadt.de [Abstractpdf] For $n \geq 2$ let $\Delta$ be a Dynkin diagram of rank $n$ and let $I = \{ 1, \ldots, n \}$ be the set of labels of $\Delta$. A group $G$ admits a {\it weak Phan system of type $\Delta$ over $\C$} if $G$ is generated by subgroups $U_i$, $i \in I$, which are central quotients of simply connected compact semisimple Lie groups of rank one, and contains subgroups $U_{i,j} = \langle U_i,U_j\rangle$, $i \neq j \in I$, which are central quotients of simply connected compact semisimple Lie groups of rank two such that $U_i$ and $U_j$ are rank one subgroups of $U_{i,j}$ corresponding to a choice of a maximal torus and a fundamental system of roots for $U_{i,j}$. It is shown in this article that $G$ then is a central quotient of the simply connected compact semisimple Lie group whose complexification is the simply connected complex semisimple Lie group of type $\Delta$. Keywords: Compact Lie groups, Tits buildings, Phantype theorems, amalgam method. MSC: 22C05, 51E24, 20E42 [ Fulltextpdf (240 KB)] for subscribers only. 