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Journal of Lie Theory 28 (2018), No. 2, 561--575
Copyright Heldermann Verlag 2018

Heisenberg Algebras from Division Algebras and Parabolic Subalgebras of Simple Lie Algebras

Aroldo Kaplan
Dept. of Mathematics, University of Massachusetts, Amherst, MA01002, U.S.A.
and: CONICET-CIEM, Universidad Nacional de Cordoba, Medina Allende, Cordoba 5000, Argentina

Mauro Subils
CONICET-FCEIA, Universidad Nacional de Rosario, Pellegrini 250, Rosario 2000, Argentina

Every real simple Lie algebra which is not compact or isomorphic to so(1,n) contains a unique standard parabolic subalgebra whose nilradical is a Heisenberg-like algebra associated to a division algebra. Some geometric consequences are discussed.

Keywords: Heisenberg, parabolic subalgebras, distributions.

MSC: 22E25, 58A30, 17C60

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