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

This article answers a question that naturally arises from the articles byGrabitz and Broussous "Pure elements and intertwining classes of simple stratain local central simple algebras" and Broussous and Lemaire "Buildings ofGL(m,D) and Centralizers". For an Azumaya-Algebra A over a non-Archimedeanlocal field F, Grabitz and Broussous have introduced embedding invariants forfield embeddings, that is for pairs (E,a), where E is a field extension of F inA, and $a$ is a hereditary order which is normalised by E^x. On the other handif we take such a field extension E and define B to be the centralizer of E inA, then G:=A^x and G_E:=B^x are sets of rational points of reductive groupsdefined over F and E respectively. Broussous and Lemaire have defined a mapj_E: I^{E^x}\to I_E, where $I$ is the the Euclidean building of $G$, and I_E isthe Euclidean building of G_E. The question which we address is to relate theembedding invariants to the behavior of the map j_E with respect to thesimplicial structures of $I$ and I_E. I have to thank very much Prof. Zink fromHomboldt University Berlin for his helpful remarks, the revision of the workand for giving my the interesting task.

Embeddings of local fields in simple algebras and simplicial structures on the Bruhat-Tits building