<p style='text-indent:20px;'>The core diagram of a double Lie algebroid consists the algebroid, together with two core-anchor maps to sides algebroid. If these core-anchors are surjective, then and its called <i>transitive</i>. This paper establishes an equivalence between transitive algebroids, diagrams over fixed base manifold. In other words, it proves that is completely de...

1 Introduction: The aim of this note is to point out that Chern characters can be computed using curvatures of " connections up to homotopy " , and to present an application to the vanishing theorem for Lie algebroids. Classically, Chern characters are computed with the help of a connection and its curvature. However, one often has to relax the notion of connection so that one gains more freedo...

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.

We study the conditions that an operator, defined on the spaces of degree 0 and 1 of a Gerstenhaber or BV algebra, has to satisfy so that we can find an extension that generates the whole algebra. When applied to the Gerstenhaber or BV algebra associated to a Lie algebroid, it gives a global proof of the correspondence between BV-generators and flat connections.

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 note, we prove the equivalence of two characterizations of hypercomplex structures on Courant algebroids, one in terms of Nijenhuis concomitants and the other in terms of (almost) torsionfree connections for which each of the three complex structures is parallel. A Courant algebroid [4] consists of a vector bundle π : E → M , a nondegenerate symmetric pairing 〈, 〉 on the fibers of π, a ...