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We will prove that the generalized Lie algebroid is a distinguished exampleby Lie algebroid. The generality of it with respect to the Lie algebroid issimilar with the generality of the pull-back vector bundle with respect to thevector bundle. Next, we will prove that the proof of Theorem 3.1 from [15] is amisconception and the mentioned Theorem has no validity. Finally, we anatomizean optimal control problem solvable in the generalized Lie algebroid frameworkwhereas Lie algebroid instrumentation can not solve it.

Generalized Lie Algebroids - Examples by Distinguished Lie Algebroids with Applications to Optimal Control