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/

Zendy Plus

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

Zendy Tools

Zendy Open

Let D(e) denote the weighted Dynkin diagram of a nilpotent element $e$ incomplex simple Lie algebra $\g$. We say that D(e) is divisible if D(e)/2 isagain a weighted Dynkin diagram. (That is, a necessary condition fordivisibility is that $e$ is even.) The corresponding pair of nilpotent orbitsis said to be friendly. In this note, we classify the friendly pairs anddescribe some of their properties. We also observe that any subalgebra sl(3) in$\g$ determines a friendly pair. Such pairs are called A2-pairs. It turns outthat the centraliser of the lower orbit in an A2-pair has some remarkableproperties. Let $Gx$ be such an orbit and $h$ a characteristic of $x$. Then $h$determines the Z-grading of the centraliser $z=z(x)$. We prove that $z$ isgenerated by the Levi subalgebra $z(0)$ and two elements in $z(1)$. Inparticular, (1) the nilpotent radical of $z$ is generated by $z(1)$ and (2)$x\in [z,z]$. The nilpotent elements having the last property are calledreachable.

On divisible weighted Dynkin diagrams and reachable elements