Infinitesimally generated subsemigroups of motion groups
A Lie wedge \(W\) in the Lie algebra of a Lie group \(G\) is said to be global if there exists a closed subsemigroup \(S\) of \(G\) such that the tangent wedge \(L(S)\) of \(S\) is \(W\). The author investigates globality questions in Lie groups which are motion groups (groups of the form \(KA\) where \(K\) is a compact subgroup and \(A\) is a normal abelian subgroup). He characterizes a special class of Lie wedges called semialgebras in the Lie algebras of motion groups and gives a simple necessary and sufficient condition for globality. This condition is automatically satisfied if \(G\) is simply connected.
scientific article; zbMATH DE number 14138
scientific article