Note on two compatibility criteria: Jacobi-Mayer bracket vs. differential Gröbner basis.
On a general difference Galois theory I
We know well difference Picard-Vessiot theory, Galois theory of linear difference equations. We propose a general Galois theory of difference equations that generalizes Picard-Vessiot theory. For every difference field extension of characteristic , we attach its Galois group, which is a group of coordinate transformation.
On a general difference Galois theory II
We apply the General Galois Theory of difference equations introduced in the first part to concrete examples. The General Galois Theory allows us to define a discrete dynamical system being infinitesimally solvable, which is a finer notion than being integrable. We determine all the infinitesimally solvable discrete dynamical systems on the compact Riemann surfaces.
On a partial complex structure
On algebra bundles and pseudo-morphisms.
On characterization of Poisson and Jacobi structures
We characterize Poisson and Jacobi structures by means of complete lifts of the corresponding tensors: the lifts have to be related to canonical structures by morphisms of corresponding vector bundles. Similar results hold for generalized Poisson and Jacobi structures (canonical structures) associated with Lie algebroids and Jacobi algebroids.
On deformations of hyperbolic 3-manifolds with geodesic boundary.
On Deformations of Kähler Spaces. I.
On Differential Equations in lie Algebroids
On formal theory of differential equations. II.
On formal theory of differential equations. III.
Elements of the general theory of Lie-Cartan pseudogroups (including the intransitive case) are developed within the framework of infinitely prolonged systems of partial differential equations (diffieties) which makes it independent of any particular realizations by transformations of geometric object. Three axiomatic approaches, the concepts of essential invariant, subgroup, normal subgroup and factorgroups are discussed. The existence of a very special canonical composition series based on Cauchy...
On graded algebra bundles.
On infinite Lie groups
Under some regularity conditions one proves that quotients and kernels of infinitesimal analytic Lie pseudo-groups by invariant fiberings are again infinitesimal Lie pseudo-groups. The regularity conditions are shown to be necessary and sufficient if one wishes both quotient and kernel to be infinitesimal Lie pseudo-groups. One defines and proves the existence of the quotient of an infinitesimal Lie pseudo-group by a normal sub-pseudo group. An equivalence relation for germs of infinitesimal Lie...
On infinitesimal isometries of a hypersurface
On Lie algebroid actions and morphisms
On mappings of a manifold into a Lie group
On Martin Bordemann's proof of the existence of projectively equivariant quantizations
The paper explains the notion of projectively equivariant quantization. It gives a sketch of Martin Bordemann's proof of the existence of projectively equivariant quantization on arbitrary manifolds.
On spectra of geometric operators on open manifolds and differentiable groupoids.
On the cohomology of vector fields on parallelizable manifolds
In the present paper we determine for each parallelizable smooth compact manifold the second cohomology spaces of the Lie algebra of smooth vector fields on with values in the module . The case of is of particular interest since the gauge algebra of functions on with values in a finite-dimensional simple Lie algebra has the universal central extension with center , generalizing affine Kac-Moody algebras. The second cohomology classifies twists of the semidirect product of with the...
On the equivalence of variational problems. III