6533b7cefe1ef96bd1257203
RESEARCH PRODUCT
A class of nilpotent Lie algebras admitting a compact subgroup of automorphisms
Rory BiggsGiovanni Falconesubject
Discrete mathematicsPure mathematicsOscillator algebra010102 general mathematicsUniversal enveloping algebra010103 numerical & computational mathematics01 natural sciencesAffine Lie algebraLie conformal algebraGraded Lie algebraNilpotent Lie algebraComputational Theory and MathematicsLie algebraCompact Lie algebraSettore MAT/03 - GeometriaGeometry and Topology0101 mathematicsCompact derivationGeneralized Kac–Moody algebraAnalysisMathematicsdescription
Abstract The realification of the ( 2 n + 1 ) -dimensional complex Heisenberg Lie algebra is a ( 4 n + 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-10-01 | Differential Geometry and its Applications |