Biggs, RoryFalcone, Giovanni2018-04-062017-10Biggs, R. & Falcone, G. 2017, 'A class of nilpotent Lie algebras admitting a compact subgroup of automorphisms', Differential Geometry and its Applications, vol. 54, part A, pp. 251-263.0926-2245 (print)1872-6984 (online)10.1016/j.difgeo.2017.04.009http://hdl.handle.net/2263/64408The realification of the (2n + 1)-dimensional complex Heisenberg Lie algebra is a (4n + 2) -dimensional real nilpotent Lie algebra with a 2-dimensional commutator ideal coinciding with the centre, and admitting the compact algebra of sp(n) derivations. We investigate, in general, whether a real nilpotent Lie algebra with 2-dimensional commutator ideal coinciding with the centre admits a compact Lie algebra of derivations. This also gives us the occasion to revisit a series of classic results, with the expressed aim of attracting the interest of a broader audience.en© 2017 Elsevier B.V. All rights reserved. Notice : this is the author’s version of a work that was accepted for publication in Differential Geometry and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. A definitive version was subsequently published in Differential Geometry and its Applications, vol. 54, part A, pp. 251-263, 2017. doi : 10.1016/j.difgeo.2017.04.009.Oscillator algebraCompact derivationLie algebrasAutomorphismsPostprint Article