Given a G-structure with connection satisfying regularity assumption we associate to it classifying Lie algebroid. This algebroid contains all the information about equivalence problem and is an example of We discuss properties this algebroid, groupoids integrating relationship Cartan’s realization problem.

A notion of an algebroid-a generalization of a Lie algebroid structure on a vector bundle is introduced. We show that many objects of the differential calculus on a manifold M associated with the canonical Lie algebroid structure on TM can be obtained in the framework of a general algebroid. Also a compatibility condition which leads, in general, to a concept of a bialgebroid. 0 Introduction. T...

As a continuation of previous papers, we study the concept of a Lie algebroid structure on an affine bundle by means of the canonical immersion of the affine bundle into its bidual. We pay particular attention to the prolongation and various lifting procedures, and to the geometrical construction of Lagrangian-type dynamics on an affine Lie algebroid.

A VB–algebroid is essentially defined as a Lie algebroid object in the category of vector bundles. There is a one-to-one correspondence between VB–algebroids and certain flat Lie algebroid superconnections, up to a natural notion of equivalence. In this setting, we are able to construct characteristic classes, which in special cases reproduce characteristic classes constructed by Crainic and Fe...

It is well-known that the category of comodules over a flat Hopf algebroid is abelian but typically fails to have enough projectives, and more generally, the category of graded comodules over a graded flat Hopf algebroid is abelian but typically fails to have enough projectives. In this short paper we prove that the category of connective graded comodules over a connective, graded, flat, finite...

Axioms of Lie algebroid are discussed. In particular, it is shown that a Lie QD-algebroid (i.e. a Lie algebra bracket on the C∞(M)-module E of sections of a vector bundle E over a manifold M which satisfies [X, fY ] = f [X, Y ] + A(X,f)Y for all X, Y ∈ E , f ∈ C∞(M), and for certain A(X,f) ∈ C∞(M)) is a Lie algebroid if rank(E) > 1, and is a local Lie algebra in the sense of Kirillov if E is a ...

In this paper, we study deformations of coisotropic submanifolds in a symplectic manifold. First we derive the equation that governs C∞ deformations of coisotropic submanifolds and define the corresponding C∞-moduli space of coisotropic submanifolds modulo the Hamiltonian isotopies. This is a non-commutative and non-linear generalization of the well-known description of the local deformation sp...

We recall the concept of a Lie algebroid on a vector bundle and the associated notion of Lagrange-type equations. A heuristic calculus of variations approach tells us what a time-dependent generalization of such equations should look like. In order to find a geometrical model for such a generalization, the idea of a Lie algebroid structure on a class of affine bundles is introduced. We develop ...

The notion of Leibniz algebroid is introduced, and it is shown that each Nambu-Poisson manifold has associated a canonical Leibniz algebroid. This fact permits to define the modular class of a Nambu-Poisson manifold as an appropiate cohomology class, extending the well-known modular class of Poisson manifolds.

We discuss relations of linear Nambu-Poisson structures to Filippov algebras and define a Filippov algebroid – a generalization of a Lie algebroid. We also prove results describing multiplicative Nambu-Poisson structures on Lie groups. In particular, it is shown that simple Lie groups do not admit multiplicative Nambu-Poisson structures of order > 2.