Dietrich Burde
Crystallographic actions on Lie groups and post-Lie algebra structures
Crystallographic groups and crystallographic actions have a long history, starting with the famous list by Hilbert in 1900 asking about Euclidean crystallographic groups. Since then many generalizations have been studied, among them affine and nil-affine crystallographic actions. It turns out that these actions can be understood on the level of Lie-algebraic structures, in particular of pre- and post-Lie algebra structures on Lie algebras. We present several results on the existence and classification of such structures, for semisimple and reductive Lie groups, but also for solvable and nilpotent ones.
