
Journal of Lie Theory 30 (2020), No. 4, 981996 Copyright Heldermann Verlag 2020 A Different Perspective on Hlike Lie Algebras Cathy Kriloff Dept. of Mathematics and Statistics, Idaho State University, Pocatello, ID 832098085, U.S.A. krilcath@isu.edu Tracy Payne Dept. of Mathematics and Statistics, Idaho State University, Pocatello, ID 832098085, U.S.A. payntrac@isu.edu We characterize Hlike Lie algebras in terms of subspaces of cones over conjugacy classes in R^{q}, translating the classification problem for Hlike Lie algebras to an equivalent problem in linear algebra. We study properties of Hlike Lie algebras, present new methods for constructing them, including tensor products and central sums, and we classify Hlike Lie algebras whose associated J_{Z}maps have real rank two for all nonzero Z. Keywords: nilmanifold, Htype, Hlike, Heisenberg type, Heisenberg algebra. MSC: 53C30, 22E25. [ Fulltextpdf (167 KB)] for subscribers only. 