Abstract
We examine what it means to say that certain endomorphisms of a factor (which we call equi-modular) are extendable. We obtain several conditions on an equi-modular endomorphism, and single out one of them with a purely ‘subfactor flavour’ as a theorem. We then exhibit the obvious example of endomorphisms satisfying the condition in this theorem. We use our theorem to determine when every endomorphism in an E0-semigroup on a factor is extendable: this property is easily seen to be a cocycle-conjugacy invariant of the E0-semigroup. We conclude by giving examples of extendable E0-semigroups, and by showing that the Clifford flows on the hyperfinite II1 factor are not extendable, neither are the free flows.
