I want to understand this passage on the articule: Ping Xu. "Momentum Maps and Morita Equivalence".
By $A → P$ we denote the Lie algebroid of $Γ\rightrightarrows P$, where the anchor map is denoted by $a : A → TP$. For any $ξ ∈ Γ(A)$, by $\overrightarrow{\xi}$ and $\overleftarrow{\xi}$ we denote its corresponding right-and left-invariant vector fields on Γ respectively.
why does every section $ξ ∈ Γ(A)$ have a vector field on $Γ$ and why do we have two, a right invariant and a lerf invariant vector fields? Thank you!