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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We prove that a discrete subgroup generated by two lattices in oppositeminimal horospherical subgroups of $SL(3,\mathbb{C})$ is arithmetic and thus bya Borel and Harish-Chandra also a lattice. We follow the method and ideas usedby Oh in \cite{Ref13}. There, Oh proves the same result for lattices in minimalhorospherical subgroups of $SL(n,\mathbb{R})$. The method consists of studyingthe orbits of the generating lattices in the horospherical subgroups under theconjugation action of the commutator of the corresponding Levi subgroup inorder to obtain a rational structure for $SL(3,\mathbb{C})$. A theorem ofRatner reduces the possibilities for the closure of the orbits. Then, by thediscreteness of the generated subgroup, it can be shown the closeness of theorbits. Finally, using this information, it's possible to find a rational formsuch that the subgroup generated by the lattices is arithmetic.

Discrete subgroups generated by lattices in opposite horospherical subgroups of $SL(3,\mathbb{C})$ following Hee Oh