Translations in simply transitive affine actions of 5-dimensional nilpotent Lie groups. (Q1426483)

The authors study simply transitive affine actions of Lie groups on Euclidean space \({\mathbb R}^n\); especially for the case in which the Lie groups are 5-dimensional nilpotent groups. The work is associated with a conjecture by \textit{L. Auslander} [Am. J. Math. 99, 809--826 (1977; Zbl 0357.22006)], which implies a possible classification of all simply transitive affine actions of a given nilpotent Lie group in an iterative way. This paper considers the simply transitive actions without non-trivial translations in the 5-dimensional case. The authors give a complete classification of all possible such actions by translating the original problem in terms of complete left symmetric structures on the corresponding Lie algebra.