Some generalizations of the notion of Lie algebra

We introduce the notion of left (and right) quasi-Loday algebroids and a "universal space" for them, called a left (right) omni-Loday algebroid, in such a way that Lie algebroids, omni-Lie algebras and omni-Loday algebroids are particular substructures.Comment: Second version. 14 pages. Included some comments about previous works related to Leibniz algebras, and updated bibliography. A new example adde

On Lie Algebroids and Poisson Algebras

We introduce and study a class of Lie algebroids associated to faithful modules which is motivated by the notion of cotangent Lie algebroids of Poisson manifolds. We also give a classification of transitive Lie algebroids and describe Poisson algebras by using the notions of algebroid and Lie connections