A class of nilpotent Lie algebras admitting a compact subgroup of automorphisms

作者：Biggs Rory; Falcone Giovanni^*

来源：Differential Geometry and its Applications, 2017, 54: 251-263.

DOI：10.1016/j.difgeo.2017.04.009

• Oscillator algebra
• Compact derivation

The 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 sp(n) of 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.

• 出版日期2017-10