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.
"An Approach to Omni-Lie Algebroids Using Quasi-Derivations." J. Gen. Lie Theory Appl. 5 1 - 10, 2011. https://doi.org/10.4303/jglta/G100801