Affine structures on 4-step nilpotent Lie algebras
The authors introduce a new method for constructing minimal affine representations of Lie algebras. This method, using polynomial constructions, relates to one in group theory developed by \textit{I. B. S. Passi} [J. Algebra 16, 121-151 (1968; Zbl 0159.31502)]. In particular, for certain nilpotent Lie algebras of class-4, modules are constructed which show the existence of complete left-symmetric structures and minimal faithful affine representations. This construction has bearing on the problem of groups being realized as fundamental groups of compact, complete affinely flat manifolds [cf. \textit{J. Milnor}, Adv. Math. 25, 178-187 (1977; Zbl 0364.55001)].
scientific article; zbMATH DE number 1061803