
Journal of Lie Theory 21 (2011), No. 3, 711727 Copyright Heldermann Verlag 2011 Characterizations of Heisenberglike Lie Algebras Rachelle C. DeCoste Dept. of Mathematics and Computer Science, Wheaton College, Norton, MA 02766, U.S.A. decoste_rachelle@wheatoncollege.edu Lisa DeMeyer Dept. of Mathematics, Central Michigan University, Mount Pleasant, MI 48858, U.S.A. lisa.demeyer@cmich.edu Maura B. Mast Dept. of Mathematics, University of Massachusetts, Boston, MA 021253393, U.S.A. maura.mast@umb.edu We obtain characterizations of Heisenberglike Lie algebras which are generalizations of results on Lie algebras of Heisenberg type, including a characterization for Heisenberglike Lie algebras in terms of the curvature transformation. We also establish infinite families of examples of Lie algebras which are Heisenberglike, but not Heisenberg type, including examples arising from representations of su(2). Keywords: Nilpotent Lie algebras, Nilpotent Lie groups, Heisenberg type Lie algebra, Heisenberglike Lie algebra. MSC: 53C30; 22E25 [ Fulltextpdf (282 KB)] for subscribers only. 