Constructs the first examples of separable II₁ factors with no non-trivial crossed product decompositions via a novel embedding property into the tensor square.
Type II$_1$ factors with arbitrary countable endomorphism group
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abstract
In \cite{Ioana:vNsuperrigidity}, Ioana introduced three new invariants of type II$_1$ factors: the one-sided fundamental group, the endomorphism semigroup and the set of right-finite bimodules. In \cite{Ioana:vNsuperrigidity}, he does not provide many computations of these invariants. In particular, the question whether these invariants can be trivial is left open. We give an explicit example of a type II$_1$ factor for which all three invariants are trivial. More generally, for any countable left-cancellative semigroup $G$, we construct a type II$_1$ factor $M$ whose endomorphism semigroup is precisely $G$.
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A class of II$_1$ factors without non-trivial crossed product decompositions
Constructs the first examples of separable II₁ factors with no non-trivial crossed product decompositions via a novel embedding property into the tensor square.