English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We prove that $L(SL_2(\textbf{k}))$ is a maximal Haagerup von Neumannsubalgebra in $L(\textbf{k}^2\rtimes SL_2(\textbf{k}))$ for$\textbf{k}=\mathbb{Q}$. Then we show how to modify the proof to handle$\textbf{k}=\mathbb{Z}$. The key step for the proof is a complete descriptionof all intermediate von Neumann subalgebras between $L(SL_2(\textbf{k}))$ and$L^{\infty}(Y)\rtimes SL_2(\textbf{k})$, where$SL_2(\textbf{k})\curvearrowright Y$ denotes the quotient of the algebraicaction $SL_2(\textbf{k})\curvearrowright \widehat{\textbf{k}^2}$ by modding outthe relation $\phi\sim \phi'$, where $\phi$, $\phi'\in \widehat{\textbf{k}^2}$and $\phi'(x, y):=\phi(-x, -y)$ for all $(x, y)\in \textbf{k}^2$. As aby-product, we show $L(PSL_2(\mathbb{Q}))$ is a maximal von Neumann subalgebrain $L^{\infty}(Y)\rtimes PSL_2(\mathbb{Q})$; in particular,$PSL_2(\mathbb{Q})\curvearrowright Y$ is a prime action, i.e. it admits nonon-trivial quotient actions.

Maximal Haagerup subalgebras in $L(\mathbb{Z}^2\rtimes SL_2(\mathbb{Z}))$