We give a formulation of certain types of mechanical systems using the structure of groupoid of the tangent and cotangent bundles to the connguration manifold M; the set of units is the zero section identiied with the manifold M. We study the Legendre transformation on Lie algebroids. The purpose of this paper is not to prove new results but to investigate certain elementary tools utilized in A...

In this note a functorial approach to the integration problem of an LAgroupoid to a double Lie groupoid is discussed. To do that, we study the notions of fibered products in the categories of Lie groupoids and Lie algebroids, giving necessary and sufficient conditions for the existence of such. In particular, it turns out, that the fibered product of Lie algebroids along integrable morphisms is...

In this note a functorial approach to the integration problem of an LAgroupoid to a double Lie groupoid is discussed. To do that, we study the notions of fibred products in the categories of Lie groupoids and Lie algebroids, giving necessary and sufficient conditions for the existence of such. In particular, it turns out, that the fibred product of Lie algebroids along integrable morphisms is a...

We first investigate the algebraic structure of vertex algebroids B when are simple Leibniz algebras. Next, we use these to construct indecomposable non-simple C2-cofinite N-graded algebras VB?. In addition, classify irreducible VB?-modules and examine conformal vectors