6 papers
The index of subalgebras and strange coadjoint orbits
Dmitri I. Panyushev
For an algebraic group with , we develop a method for estimating the index of a subalgebra in via the use of coadjoint…
Near-derivations and their applications to Lie algebras
Dmitri Panyushev, Oksana Yakimova
E.B. Vinberg's theory of quasi-derivations of algebras is extended to a broader framework of near-derivations. This deepens connections between Poisson geometry and Lie theory. Alt…
Horospherical splittings of and related Poisson commutative subalgebras of
Dmitri Panyushev, Oksana Yakimova
Let a Lie algebra be a linear sum of two complementary subalgebras and . We continue our investigations initiated in (J. London Math. Soc.…
Invariants of twisted current algebras and related Poisson-commutative subalgebras
Dmitri Panyushev, Oksana Yakimova
Let q be a finite-dimensional Lie algebra and an automorphism of q of order m. We extend to an automorphism of the loop algebra of q and consider the fixed-point subalgeb…
Nilpotent orbits and their secant varieties
Dmitri I. Panyushev
Let be a simple algebraic group and a nilpotent orbit in . Let denote the affine cone over the secant variety of $\overlin…
Projections of nilpotent orbits in a simple Lie algebra and shared orbits
Dmitri I. Panyushev
Let be a simple algebraic group with and a nilpotent orbit. If is a reductive subgroup of with ,…