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Transitivity of families of invariant vector fields on the semidirect products of Lie groups

1982
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Transactions of the American Mathematical Society
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In this paper we give necessary and sufficient conditions for a family of right (or left) invariant vector fields on a Lie group G to be transitive. The concept of transitivity is essentially that of controllability in the literature on control systems. We consider families of right (resp. left) invariant vector fields on a Lie group G which is a semidirect product of a compact group K and a vector space V on which K acts linearly. If 5F is a family of right-invariant vector fields, then the

doi:10.1090/s0002-9947-1982-0654849-4
fatcat:ttqkzu4horfgbfduadhjn2sbxe