TWISTED CONJUGACY CLASSES IN LATTICES IN SEMISIMPLE LIE GROUPS

Given a group automorphism I center dot: I" -> aEuro parts per thousand I", one has an action of I" on itself by I center dot-twisted conjugacy, namely, g.x = gxI center dot(g (-1)). The orbits of this action are called I center dot-conjugacy classes. One says that I" has the Ra-property if there are infinitely many I center dot-conjugacy classes for every automorphism I center dot of I". In this paper we show that any irreducible lattice in a connected semisimple Lie group having finite centre and rank at least 2 has the Ra-property.