Type II₁ factors with arbitrary countable endomorphism group

2013/01/11 by Steven Deprez, Deprez, Steven
Computer Science · Mathematics · #20M20 (Secondary) #28D15 #46L36 (Primary) 37A20 #46L40 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1301.2618

openalex publication_date 2013/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In \citeIoana:vNsuperrigidity, Ioana introduced three new invariants of type II₁ factors: the one-sided fundamental group, the endomorphism semigroup and the set of right-finite bimodules. In \citeIoana: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 II₁ factor for which all three invariants are trivial. More generally, for any countable left-cancellative semigroup G, we construct a type II₁ factor M whose endomorphism semigroup is precisely G.

Citations

• A class of superrigid group von Neumann algebras

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