Simply connected lie subgroups of the unipotent Lie group of order 4

Abstract

In this paper we obtain simply connected Lie subgroups (up to isomorphism) of the Lie group G4 of upper triangular matrices of order 4 having “1” in its main diagonal. To do it, we determine Lie subalgebras of the Lie algebra g4 associated with G4. We find that there exist 4 simply connected subgroups of G4 for dimension less than 4, 3 for dimension 4 and 4 for dimension 5. We also prove that the rest of groups associated with Lie algebras of these dimensions are not representable as subgroups of G4.