Rings of Invariant Polynomials for a Class of Lie Algebras

DOI10.2307/1995803zbMath0232.22027OpenAlexW4235119703WikidataQ56384844 ScholiaQ56384844MaRDI QIDQ5639952

S. J. Takiff

Publication date: 1971

Full work available at URL: https://doi.org/10.2307/1995803

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Related Items

Poisson enveloping algebras and the Poincaré-Birkhoff-Witt theorem, Multi-graded Galilean conformal algebras, Koszul duality for semidirect products and generalized Takiff algebras, On the coadjoint representation of \(\mathbb Z_2\)-contractions of reductive Lie algebras, Asymmetric Galilean conformal algebras, LIE ALGEBRA MODULES WHICH ARE LOCALLY FINITE AND WITH FINITE MULTIPLICITIES OVER THE SEMISIMPLE PART, Invariant polynomials on truncated multicurrent algebras, Symmetric invariants related to representations of exceptional simple groups, Whittaker modules and quasi-Whittaker modules for the Euclidean Lie algebra \(\mathfrak{e}(3)\), Simple modules over the Takiff Lie algebra for sl2, Category \(\mathcal{O}\) for Takiff Lie algebras, Nonassociative rings, Highest-weight theory for truncated current Lie algebras, Semi-Direct Products Involving Sp2n or Spinn with Free Algebras of Symmetric Invariants, Casimir elements and Sugawara operators for Takiff algebras, \((\mathfrak{gl}_M, \mathfrak{gl}_N)\)-dualities in Gaudin models with irregular singularities, Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems, Lie groups and homogeneous spaces, Category O for Takiff sl2, The Lie algebra of derivations of a current Lie algebra, Compatible Poisson brackets associated with 2‐splittings and Poisson commutative subalgebras of S(g), La formule de Poisson-Plancherel pour un groupe de Takiff associé à un groupe de Lie semi-simple à centre fini. (The Poisson-Plancherel formula for a Takiff group associated to a semi-simple Lie group with finite centre), A bi-Hamiltonian nature of the Gaudin algebras

Cites Work

• The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
• On the Ring of Invariant Polynomials on a Semisimple Lie Algebra
• Invariants of Finite Groups Generated by Reflections
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