19 citations · 133 across the 72 of their papers we have counts for
4 papers · 2 filters
Abelian ideals and amazing roots
Dmitri I. Panyushev
Let be a simple Lie algebra with a Borel subalgebra . To any long positive root , one associates two ideals of : the abelian ideal $I(γ)_…
Takiff algebras with polynomial rings of symmetric invariants
Dmitri Panyushev, Oksana Yakimova
Extending results of Rais-Tauvel, Macedo-Savage, and Arakawa-Premet, we prove that under mild restrictions on the Lie algebra having the polynomial ring of symmetric…
Semi-direct products of Lie algebras and covariants
Dmitri Panyushev, Oksana Yakimova
The coadjoint representation of a connected algebraic group with Lie algebra is a thrilling and fascinating object. Symmetric invariants of (= $\mat…
On seaweed subalgebras and meander graphs in type D
Dmitri Panyushev, Oksana Yakimova
In 2000, Dergachev and Kirillov introduced subalgebras of "seaweed type" in and computed their index using certain graphs, which we call type- meander gr…