  Constants of motion are calculated for 2+1 dimensional gravity with topology
R x T^2 and negative cosmological constant. Certain linear combinations of them
satisfy the anti - de Sitter algebra so(2,2) in either ADM or holonomy
variables. Quantisation is straightforward in terms of the holonomy parameters.
On inclusion of the Hamiltonian three new global constants are derived and the
quantum algebra extends to that of the conformal algebra so(2,3). The modular
group appears as a discrete subgroup of the conformal group. Its quantum action
is generated by these conserved quantities.
