Singular complete integrability
-trivial deformations of -modules of symbols.
Some division theorems for vector fields
This paper is concerned with the problem of divisibility of vector fields with respect to the Lie bracket [X,Y]. We deal with the local divisibility. The methods used are based on various estimates, in particular those concerning prolongations of dynamical systems. A generalization to polynomials of the adjoint operator (X) is given.
Some notes about -Lie algebras.
Some Remarks on Dirac Structures and Poisson Reductions
Dirac structures are characterized in terms of their characteristic pairs defined in this note and then Poisson reductions are discussed from the point of view of Dirac structures.
Subalgebras of finite codimension in symplectic Lie algebra
Subalgebras of germs of vector fields leaving fixed in , of finite codimension in symplectic Lie algebra contain the ideal of germs infinitely flat at . We give an application.
Symplectic integrators to stochastic Hamiltonian dynamical systems derived from composition methods.
The Frölicher-Nijenhuis bracket in non-commutative differential geometry.
The groups of automorphisms of the Witt and Virasoro Lie algebras
Let be a Laurent polynomial algebra over a field of characteristic zero, the Lie algebra of -derivations of the algebra , the so-called Witt Lie algebra, and let be the Virasoro Lie algebra which is a -dimensional central extension of the Witt Lie algebra. The Lie algebras and are infinite dimensional Lie algebras. We prove that the following isomorphisms of the groups of Lie algebra automorphisms hold: , and give a short proof that .
Ther Lie Algebra of Polynomial Vector Fields and the Jacobian Conjecture.
Triangular Lie bialgebras and matched pairs for Lie algebras of real vector fields on .
Two results on a class of Poisson structures on Lie groups.
Universal lifting theorem and quasi-Poisson groupoids
We prove the universal lifting theorem: for an -simply connected and -connected Lie groupoid with Lie algebroid , the graded Lie algebra of multi-differentials on is isomorphic to that of multiplicative multi-vector fields on . As a consequence, we obtain the integration theorem for a quasi-Lie bialgebroid, which generalizes various integration theorems in the literature in special cases. The second goal of the paper is the study of basic properties of quasi-Poisson groupoids. In particular,...
Variational calculus on Lie algebroids
It is shown that the Lagrange's equations for a Lagrangian system on a Lie algebroid are obtained as the equations for the critical points of the action functional defined on a Banach manifold of curves. The theory of Lagrangian reduction and the relation with the method of Lagrange multipliers are also studied.
Vector fields on the space of functions univalent inside the unit disk via Faber polynomials.
Vector form brackets in Lie algebroids.
Vector form brackets in Lie algebroids
A brief exposition of Lie algebroids, followed by a discussion of vector forms and their brackets in this context - and a formula for these brackets in “deformed” Lie algebroids.
Weitzenböck Formula on Lie Algebroids
A Weitzenböck formula for the Laplace-Beltrami operator acting on differential forms on Lie algebroids is derived.
Zig-zag dynamical systems and the Baker-Campbell-Hausdorff formula
Об алгебраической структуре алгебры Ли векторных полей на прямой