Journal of Lie Theory 21 (2011), No. 3, 711--727
Copyright Heldermann Verlag 2011
Characterizations of Heisenberg-like 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 02125-3393, U.S.A.
maura.mast@umb.edu
We obtain characterizations of Heisenberg-like Lie algebras which are generalizations of results on Lie algebras of Heisenberg type, including a characterization for Heisenberg-like Lie algebras in terms of the curvature transformation. We also establish infinite families of examples of Lie algebras which are Heisenberg-like, but not Heisenberg type, including examples arising from representations of su(2).
Keywords: Nilpotent Lie algebras, Nilpotent Lie groups, Heisenberg type Lie algebra, Heisenberg-like Lie algebra.
MSC: 53C30; 22E25
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