Infinitesimal conformal transformations of IRn are always polynomial and finitely generated when n > 2. Here we prove that the Lie algebra of infinitesimal conformal polynomial transformations over IRn, n ≥ 2, is maximal in the Lie algebra of polynomial vector fields. When n is greater than 2 and p, q are such that p+ q = n, this implies the maximality of an embedding of so(p + 1, q + 1, IR) in...

B-series originated from the work of John Butcher in the 1960s as a tool to analyze numerical integration of differential equations, in particular Runge–Kutta methods. Connections to renormalization have been established in recent years. The algebraic structure of classical Runge–Kutta methods is described by the Connes–Kreimer Hopf algebra. Lie–Butcher theory is a generalization of B-series ai...

We interpret geometrically a variant of the Robinson-Schensted correspondence which links Brauer diagrams with updown tableaux, in the spirit of Steinberg’s result [32] on the original Robinson-Schensted correspondence. Our result uses the variety of all (N , ω, V) where V is a complete flag in C2n, ω is a nondegenerate alternating bilinear form on C2n, and N is a nilpotent element of the Lie a...

We prove that for any known Lie algebra g having none invariants for the coadjoint representation, the absence of invariants is equivalent to the existence of a left invariant exact symplectic structure on the corresponding Lie group G. We also show that a nontrivial generalized Casimir invariant constitutes an obstruction for the exactness of a symplectic form, and provide solid arguments to c...

ly one can define a Lie group as a smooth manifold which is also a group such that inversion and multiplication are smooth maps. A special case we focus on is any (topologically) closed subgroup of any SL(`,R). The major examples of “classical” Lie groups are SL(n,R), SO(m,n) (with g Im,ng = Im,n), SU(m,n) (same as SO but with conjugate transpose and complex elements), and Sp(2m,R) (similar to ...

The Lie module of the group algebra FSn of the symmetric group is known to be not projective if and only if the characteristic p of F divides n. We show that in this case its nonprojective summands belong to the principal block of FSn. Let V be a vector space of dimension m over F , and let L(V ) be the n-th homogeneous part of the free Lie algebra on V ; this is a polynomial representation of ...