Brugger, Rahel

We show that for a strong extension of discrete measured groupoids $1\to\mathcal{S}\to\mathcal{G}\to\mathcal{Q}\to 1$  with $L\mathcal{G}$ a finite factor, $\mathcal{Q}$ has poperty (T) if and only if the inclusion of $L\mathcal{S}$ into $L\mathcal{G}$ is corigid. In particular, this implies that $\mathcal{G}$ has property (T) if and only if $L^\infty(X)\subset L\mathcal{G}$ is corigid.		
		
		Furthermore, we give the definition of an invariant random positive definite function on a discrete group, generalizing both the notion of an Invariant Random Subgroup and a character. We use von Neumann algebras to show that all invariant random positive definite functions on  groups with infinite conjugacy classes which integrate to the regular character are constant.
		
		We also show a rigidity result for subfactors that are normalized by a representation of a lattice $\Gamma$ in a higher rank simple Lie group with trivial center into a finite factor. This implies that every subfactor of $L\Gamma$ which is normalized by the natural copy of $\Gamma$ is trivial or of finite index

Georg-August-University Göttingen

Characters on infinite groups and rigidity

https://ediss.uni-goettingen.de/bitstream/11858/00-1735-0000-002E-E3D5-B/1/Dissertation_Brugger.pdf

Characters on infinite groups and rigidity

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Georg-August-University Göttingen