Abstract
In this paper we establish faithful affine representations for 2-step nilpotent Lie groupsG and the associated groupsG×Aut (G), which play a crucial role in the theory of infra-nilmanifolds. Afterwards, we apply the obtained results, in order to find representations of 3-step Almost-crystallographic groups. Finally, we indicate how all of this might be used to compute the second cohomology group of an Almost-crystallographic group with coefficients in a free abelian group.
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Dekimpe, K. The construction of affine structures on virtually nilpotent groups. Manuscripta Math 87, 71–88 (1995). https://doi.org/10.1007/BF02570462
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DOI: https://doi.org/10.1007/BF02570462