The exponential image of simple complex Lie groups of exceptional type (Q1105706)

Let G denote a connected reductive complex algebraic group and \(x=x_ sx_ u\) the Jordan decomposition of \(x\in G\). The author proves the following result: The element x is of the form exp X if and only if \(x_ s\) is in the identity component of the centralizer Z(x) of x in G if and only if \(x_ s\) is in the identity component of \(Z(x_ u)\). He describes an algorithm for finding representatives x of all conjugacy classes which miss im exp. For this purpose the paper contains a detailed list of representatives u of unipotent conjugacy classes such that Z(u) is not connected.