Polynomiality for the Poisson centre of truncated maximal parabolic subalgebras

2017/01/04 by Florence Fauquant-Millet, Fauquant-Millet, Florence, Polyxeni Lamprou +1
Mathematics · #16W22 #17B22 #17B35 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1701.02238

openalex publication_date 2017/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Poisson centre of truncated maximal parabolic subalgebras of a simple Lie algebra of type B, D and E₆ is a polynomial algebra. In roughly half of the cases the polynomiality of the Poisson centre was already known by a completely different method. For the rest of the cases, our approach is to construct an algebraic slice in the sense of Kostant given by an adapted pair and the computation of an improved upper bound for the Poisson centre.

Citations

• Adapted pairs and Weierstrass sections

Related

• Slices for maximal parabolic subalgebras of a semisimple Lie algebra
• The Poisson center and polynomial, maximal Poisson commutative subalgebras, especially for nilpotent Lie algebras of dimension at most seven
• On the semi-centre of a Poisson algebra
• A degree inequality for Lie algebras with a regular Poisson semi-center
• Polynomial Algebras on Coadjoint Orbits of Semisimple Lie Groups