Classification of Invariant Subalgebras in a class of factors with property (T)

Yongle Jiang; Hongyi Li

paper

Classification of Invariant Subalgebras in a class of factors with property (T)

arXiv:2601.06353

Abstract

Let $n \geq 2$ and $G_{n} = Z^{n} ⋊ S L_{n} (Z)$ . We classify all $G_{n}$ -invariant von Neumann subalgebras in $L (G_{n})$ . For $n = 2$ , this gives an alternative proof of the previous result of Jiang-Liu. For $n \geq 3$ , this gives the first class of property (T) groups without the invariant subalgebras rigidity property but invariant subalgebras in the corresponding group factors can still be classified. As a corollary, $L (G_{n})$ admits a unique maximal Haagerup $G_{n}$ -invariant von Neumann subalgebra.