Remarks on the diagonal embedding and strong 1-boundedness

Srivatsav Kunnawalkam Elayavalli

doi:10.4171/dm/918

JournalsdmVol. 28, No. 3pp. 671–681

Remarks on the diagonal embedding and strong 1-boundedness

Srivatsav Kunnawalkam Elayavalli
University of California, Los Angeles, United States of America

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Abstract

We identify a large class of hyperbolic groups whose von Neumann algebras are not strongly 1-bounded: Sela’s hyperbolic towers over $F_{2}$ subgroups. We also show that any intermediate subalgebra of the diagonal embedding of $L (F_{2})$ into its ultrapower does not have Property (T).

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Srivatsav Kunnawalkam Elayavalli, Remarks on the diagonal embedding and strong 1-boundedness. Doc. Math. 28 (2023), no. 3, pp. 671–681

DOI 10.4171/DM/918