On decompositions and transitive actions of nilpotent Lie groups (Q6638426)

The article explores the decompositions and transitive actions of nilpotent Lie groups and their Lie algebras. The study examines connections between decompositions of groups and algebras, offering insights into global and local decompositions, with a focus on exact decompositions where substructures intersect trivially.\N\NIt also addresses transitive actions of nilpotent Lie groups on two- and three-dimensional manifolds, emphasizing irreducible actions, which lack simpler transitive subgroups. Key results include proofs of globalizability for certain nilpotent cases and classifications of such groups based on solvability and reducibility. The author describes multiple decompositions and irreducible actions in higher dimensions, connecting these properties to broader structural dynamics of nilpotent Lie groups.