horizontal subbundle on lie algebroids

Providing an appropriate definition of a horizontal subbundle of a lie algebroid will lead to construction of a better framework on lie algebriods. in this paper, we give a new and natural definition of a horizontal subbundle using the prolongation of a lie algebroid and then we show that any linear connection on a lie algebroid generates a horizontal subbundle and vice versa. the same correspondence will be proved for any covariant derivative on a lie algebroid.