
Journal of Lie Theory 26 (2016), No. 4, 9911000 Copyright Heldermann Verlag 2016 Filiform Lie Algebras Without Rational Structures Naoki Kato Graduate School of Mathematical Sciences, University of Tokyo, 381 Komaba Meguroku, Tokyo 1539814, Japan knaoki@ms.utokyo.ac.jp Hamrouni and Souissi gave a sufficient condition for a family of 7dimensional filiform Lie algebras to have no rational structures and constructed an example of a 7dimensional filiform Lie algebra without rational structures explicitly. In this paper, we give a sufficient condition for arbitrarydimensional filiform Lie algebras to have no rational structures. Moreover, we consider a sufficient condition for products of filiform Lie algebras and arbitrary nilpotent Lie algebras to have no rational structures and give infinitely many new examples of nilpotent Lie algebras without rational structures. Keywords: Nilpotent Lie algebras, filiform Lie algebras, rational structures. MSC: 22E40 [ Fulltextpdf (242 KB)] for subscribers only. 