Automorphisms of order 4 of the simply connected compact Lie group \(E_ 6\) (Q1192577)

\(E_ 6\) denotes the simply connected, compact Lie group of type \(E_ 6\). The problem is to explicitly describe all automorphisms of \(E_ 6\) having order 4 and to realize the corresponding subgroups of fixed points. In other papers listed in the bibliography, the first author has dealt with automorphisms of order 2 and order 3 in the case of \(E_ 6\) as well as other exceptional Lie groups.