Resumen de A class of superrigid group von Neumann algebras

Adrian Ioana, Sorin Popa, Stefaan Vaes

• We prove that for any group G in a fairly large class of generalized wreath product groups, the associated von Neumann algebra LG completely �remembers� the group G. More precisely, if LG is isomorphic to the von Neumann algebra L? of an arbitrary countable group ?, then ? must be isomorphic to G. This represents the first superrigidity result pertaining to group von Neumann algebras.