A class of transformations of Lie groups (Q920206)

The author examines group-affine transformations, i.e. those smooth transformations of a Lie group G which permute the cosets of the 1- parameter subgroups of G; a local description of the transformations is given. The Lie group is called affinely simple if every group-affine transformation is a composition of a (left) translation, an automorphism, and - optionally - the inversion. This property can be derived from some algebraic conditions on the Lie algebra. It is shown that almost every 3- dimensional connected Lie group (with the exception of those of Bianchi type III, \(VI_ 0\), and VII) is affinely simple.