Type II$_1$ factors with arbitrary countable endomorphism group
Operator Algebras
2013-01-15 v1 Dynamical Systems
Group Theory
Abstract
In \cite{Ioana:vNsuperrigidity}, Ioana introduced three new invariants of type II 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 factor for which all three invariants are trivial. More generally, for any countable left-cancellative semigroup , we construct a type II factor whose endomorphism semigroup is precisely .
Cite
@article{arxiv.1301.2618,
title = {Type II$_1$ factors with arbitrary countable endomorphism group},
author = {Steven Deprez},
journal= {arXiv preprint arXiv:1301.2618},
year = {2013}
}