One-parameter contractions of Lie-Poisson brackets

Semi-Direct Products Involving Sp2n or Spinn with Free Algebras of Symmetric Invariants

“…Thens =g⋉V is the Z 2 -contraction of so 2n related to the symmetric pair (so 2n , gl n ). By [Y14,Theorem 4.5], this Z 2 -contraction is good and satisfies KRC. Our goal is to describe S(s) s using the known description fors.…”

“…A generic isotropy group for (D 6 , ϕ 5 ) is SL 6 , G y is connected, and g y is a Z 2 -contraction of sl 6 , the semi-direct product sp 6 ⋉V ϕ 2 , which is a good Z 2 -contraction [Y14,Theorem 4.5].…”

“…Let ∆ k ∈ S(sp 2n+m ) be the sum of the principal k-minors and let ∆ • k be the highest V -component of ∆ k . The elements ∆ • k with even k, 2m < k 2n+m, belong to a set of the algebraically independent generators of S(s)s, see [Y14,Theorem 4.5]. For a generic point x ∈ V * , their restrictions ∆ • k |g +x form a generating set for the symmetric invariants of (sp 2n ) x = sp 2n−m .…”

Takiff Algebras With Polynomial Rings of Symmetric Invariants

“…But one can look at the canonical truncation of q, where the situation improves considerably. Following [Y14,Sect. 5], consider…”

On maximal commutative subalgebras of Poisson algebras associated with involutions of semisimple Lie algebras

“…. , f l are algebraically independent homogeneous generators of k[k * ] K , then l i=1 deg f i = b(k) [14,25,26].…”