Let  be an n-dimensional Riemannian manifold, and  be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation  induces an infinitesimal homothetic transformation on .  Furthermore,  the correspondence   gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on  onto the Lie algebra of infinitesimal ...

This paper presents an operator calculus approach to computing with non-commutative variables. First, we recall the product formulation of formal exponential series. Then we show how to formulate canonical boson calculus on formal series. This calculus is used to represent the action of a Lie algebra on its universal enveloping algebra. As applications, Hamilton's equations for a general Hamilt...

Let X and Y be finite-type CW–complexes (X connected, Y simply connected), such that the rational cohomology ring of Y is a k–rescaling of the rational cohomology ring of X . Assume H∗(X,Q) is a Koszul algebra. Then, the homotopy Lie algebra π∗(ΩY ) ⊗ Q equals, up to k–rescaling, the graded rational Lie algebra associated to the lower central series of π1(X). If Y is a formal space, this equali...

Symplectic integrators are numerical integration schemes for hamiltonian systems. The integration step is an explicit symplectic map. We find symplectic integrators using universal exponential identities or relations among formal Lie series. We give here general methods to compute such identities in a free Lie algebra. We recover by these methods all the previously known symplectic integrators ...