Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

On the uniqueness of arithmetic structures

F. E. A. Johnsona1

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)