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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.

Lisa DeMeyer
Dept. of Mathematics, Central Michigan University, Mount Pleasant, MI 48858, U.S.A.

Maura B. Mast
Dept. of Mathematics, University of Massachusetts, Boston, MA 02125-3393, U.S.A.

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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