Strong solidity of group factors from lattices in SO(n,1) and SU(n,1)

We show that the group factors LΓ, where Γ is an ICC lattice in either SO(n,1) or SU(n,1), n⩾2, are strongly solid in the sense of Ozawa and Popa (2010) [13], . This strengthens a result of Ozawa and Popa (2010) [14] showing that these factors do not have Cartan subalgebras.