Journal of Lie Theory 30 (2020), No. 4, 981--996
Copyright Heldermann Verlag 2020
A Different Perspective on H-like Lie Algebras
Cathy Kriloff
Dept. of Mathematics and Statistics, Idaho State University, Pocatello, ID 83209-8085, U.S.A.
krilcath@isu.edu
Tracy Payne
Dept. of Mathematics and Statistics, Idaho State University, Pocatello, ID 83209-8085, U.S.A.
payntrac@isu.edu
We characterize H-like Lie algebras in terms of subspaces of cones over conjugacy classes in Rq, translating the classification problem for H-like Lie algebras to an equivalent problem in linear algebra. We study properties of H-like Lie algebras, present new methods for constructing them, including tensor products and central sums, and we classify H-like Lie algebras whose associated JZ-maps have real rank two for all nonzero Z.
Keywords: nilmanifold, H-type, H-like, Heisenberg type, Heisenberg algebra.
MSC: 53C30, 22E25.
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