a1 Department of Mathematics, University College London, Gower Street, London WC1E6BT, U. K.
Margulis has given conditions under which a lattice in a semisimple Lie group admits the structure of an arithmetic subgroup. We show that these arithmetic structures are unique. The result is not subject to the condition “rkR(G) ≧ 2” required by the Margulis result. In the lowest dimensions, the result has previously been observed by Takeuchi, Maclachlan and Reid.
(Received September 28 1992)
(Revised July 12 1993)