Strong solidity of group factors from lattices in SO(n,1) and SU(n,1)

TL;DR

This paper proves that the von Neumann algebra factors arising from ICC lattices in SO(n,1) and SU(n,1) are strongly solid, extending previous results about their structural properties and absence of Cartan subalgebras.

Contribution

It establishes the strong solidity of group factors from lattices in SO(n,1) and SU(n,1), advancing understanding of their rigidity and structural features.

Findings

Group factors from ICC lattices in SO(n,1) and SU(n,1) are strongly solid.

These factors do not admit Cartan subalgebras.

The result enhances the classification of von Neumann algebras from these lattices.

Abstract

We show that the group factors of ICC lattices in either SO(n,1) or SU(n,1), n \geq 2, are strongly solid in the sense of Ozawa and Popa. This strengthens a result of Ozawa and Popa showing that these factors do not have Cartan subalgebras.