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An exponential representation of the Jordanian matrix quantum group GLh (2) is constructed in explicit form by the generators of the classical Lie algebra sl * (2,C ).

The Heisenberg algebra h(3) is the Lie algebra of the Lie group H(3) of 3*3 upper triangular matrices with the 1's on the diagonal. This group is quantized. The dual algebra h(3)* is also quantized, resulting in a quantum coadjoint representation of the quantum group H(3)a,b,c,d,m,n. The phase space T*H(3) is also quantized.

A BCH formula for groups having faithful matrix representations is derived, by a decomposition of the general group element exp(M) into factors, each factor being an exponential involving the infinitesimal generators of the group. This is a generalization of the authors earlier work for SU(3).

Using Baker-Campbell-Hausdorff formulae for the exponentials of the generators of the SU2 and SU(1,1) groups, the matrix elements of spherical and hyperbolic rotations are calculated in the angular momentum basis.

The anticommutator analogue of the Baker-Hausdorff lemma is formulated and proved by the differential equation method. It is pointed out that this analogue, when suitably transformed, is more convenient for application whenever the operators in question satisfy simpler repeated anticommutator than repeated commutator relations.