The action of a compact Lie group on nilpotent Lie algebras of type {n,2}
classification
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keywords
algebrasnilpotentgrouptypeactionadmittingautomorphismscentral
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We classify finite-dimensional nilpotent Lie algebras with $2$-dimensional central commutator ideals admitting a Lie group of automorphisms isomorphic to $SO_2(\mathbb R)$. This enables one to enlarge the class of nilpotent Lie algebras of type {n,2}.
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