We classify finite-dimensional real nilpotent Lie algebras with 2-dimensional central commutator ideals admitting a Lie group of automorphisms isomorphic to SO2(ℝR). This is the first step to extend the class of nilpotent Lie algebras of type {n,2} to solvable Lie algebras in which has codimension one.
Falcone, G., Figula, Á. (2015). The action of a compact Lie group on nilpotent Lie algebras of type n,2. FORUM MATHEMATICUM, 28(4), 795-806 [10.1515/forum-2014-0170].
The action of a compact Lie group on nilpotent Lie algebras of type n,2
FALCONE, Giovanni;
2015-01-01
Abstract
We classify finite-dimensional real nilpotent Lie algebras with 2-dimensional central commutator ideals admitting a Lie group of automorphisms isomorphic to SO2(ℝR). This is the first step to extend the class of nilpotent Lie algebras of type {n,2} to solvable Lie algebras in which has codimension one.
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