A Lie Group which has a simply connected covering group Homeomorphic to . The prototype is any connected closed subgroup of upper Triangular Complex Matrices. The Heisenberg Group is such a group.
See also Heisenberg Group, Lie Group
Knapp, A. W. ``Group Representations and Harmonic Analysis, Part II.'' Not. Amer. Math. Soc. 43, 537-549, 1996.