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 Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Let L be a finite dimensional Lie algebra over an algebraically closed fieldk of characteristic zero. We provide necessary and also some sufficientconditions in order for its Poisson center and semi-center to be polynomialalgebras over k. This occurs for instance if L is quadratic of index 2 with Lnot equal to [L,L] and also if L is nilpotent of index at most 2. The converseholds for filiform Lie algebras of type Ln, Qn, Rn and Wn. We also show howDixmier's fourth problem for an algebraic Lie algebra L can be reduced to thatof its canonical truncation. Moreover, Dixmier's statement holds for all Liealgebras of dimension at most eight. The nonsolvable, indecomposable ones amongthem possess a polynomial Poisson center and semi-center.

The polynomiality of the Poisson center and semi-center of a Lie algebra and Dixmier's fourth problem