Integrates Lax pair equations for a specific Lie algebra.
problem Low-dimensional Lie algebras of infinitesimal character .
method Shows complete integrability of Lax pair equations.
result Proves complete integrability for certain Lie algebras.
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5 results for “Connes-Kreimer”
Using a cell model for the little discs operad in terms of spineless cacti we give a minimal common topological operadic formalism for three a priori disparate algebraic structures: (1) a solution to Deligne's conjecture on the Hochschild complex, (2) the Hopf algebra of Connes and Kreimer, and (3) the string topology …
We relate the author's Lie cobracket in the module additively generated by loops on a surface with the Connes-Kreimer Lie bracket in the module additively generated by trees. To this end we introduce a pre-Lie coalgebra and a (commutative) Hopf algebra of pointed loops on a surface. In the last version I added sections…
New algebraic approach for approximating Hamiltonian dynamics.
problem Approximating Hamilton-Jacobi solutions on symplectic groupoids.
method Introducing a pre-Lie algebra and Butcher trees for symplectic groupoids.
result New class of Poisson integrators for Hamiltonian dynamics.
Lie-Butcher (LB) series are formal power series expressed in terms of trees and forests. On the geometric side LB-series generalizes classical B-series from Euclidean spaces to Lie groups and homogeneous manifolds. On the algebraic side, B-series are based on pre-Lie algebras and the Butcher-Connes-Kreimer Hopf algebra…