On the coadjoint representation of \(\mathbb Z_2\)-contractions of reductive Lie algebras
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Publication:2370167
DOI10.1016/j.aim.2006.12.011zbMath1177.17010arXivmath/0610493OpenAlexW2081704137MaRDI QIDQ2370167
Publication date: 22 June 2007
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0610493
Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Simple, semisimple, reductive (super)algebras (17B20) Group actions on affine varieties (14R20)
Related Items (28)
Jordan-Kronecker invariants of finite-dimensional Lie algebras ⋮ Weierstrass sections for some truncated parabolic subalgebras ⋮ Commuting involutions and degenerations of isotropy representations ⋮ Surprising properties of centralisers in classical Lie algebras ⋮ Parabolic contractions of semisimple Lie algebras and their invariants ⋮ Semi-direct products of Lie algebras and covariants ⋮ Commutativity of the centralizer of a subalgebra in a universal enveloping algebra ⋮ A generalization of Veldkamp's theorem for a class of Lie algebras ⋮ Symmetric invariants related to representations of exceptional simple groups ⋮ \(\mathbb{Z}_2\)-contractions of classical Lie algebras and symmetric polynomials ⋮ Takiff algebras with polynomial rings of symmetric invariants ⋮ On maximal commutative subalgebras of Poisson algebras associated with involutions of semisimple Lie algebras ⋮ Jordan-Kronecker invariants of Lie algebra representations and degrees of invariant polynomials ⋮ The Poisson center and polynomial, maximal Poisson commutative subalgebras, especially for nilpotent Lie algebras of dimension at most seven ⋮ Automorphisms of finite order, periodic contractions, and Poisson-commutative subalgebras of \({\mathcal{S}}(\mathfrak{g})\) ⋮ Polynomiality of invariants, unimodularity and adapted pairs ⋮ A remarkable contraction of semisimple Lie algebras ⋮ One-parameter contractions of Lie-Poisson brackets ⋮ Enhanced adjoint actions and their orbits for the general linear group ⋮ Semi-Direct Products Involving Sp2n or Spinn with Free Algebras of Symmetric Invariants ⋮ Center of infinitesimal Cherednik algebras of 𝔤𝔩_{𝔫} ⋮ The polynomiality of the Poisson center and semi-center of a Lie algebra and Dixmier's fourth problem ⋮ A degree inequality for Lie algebras with a regular Poisson semi-center ⋮ Periodic automorphisms of Takiff algebras, contractions, and \(\theta \)-groups ⋮ Periodic automorphisms, compatible Poisson brackets, and Gaudin subalgebras ⋮ Computing invariants and semi-invariants by means of Frobenius Lie algebras ⋮ Compatible Poisson brackets associated with 2‐splittings and Poisson commutative subalgebras of S(g) ⋮ A bi-Hamiltonian nature of the Gaudin algebras
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