This　paper　investigates　a　universal　PBW-basis　and　a　minimal　set　of　generators　for　the　Hall　algebra　H(C2(P)),　where　C2(P)　is　the　category　of　morphisms　between　projective　objects　in　a　finitary　hereditary　exact　category　A.　When　A　is　the　representation　category　of　a　Dynkin　quiver,　we　develop　multiplication　formulas　for　the　degenerate　Hall　Lie　algebra　L,　which　is　spanned　by　isoclasses　of　indecomposable　objects　in　C2(P).　As　applications,　we　demonstrate　that　L　contains　a　Lie　subalgebra　isomorphic　to　the　central　extension　of　the　Heisenberg　Lie　algebra　and　construct　the　Borel　subalgebra　of　the　simple　Lie　algebra　associated　with　A　as　a　Lie　subquotient　algebra　of　L.　©　Institute　of　Mathematics,　Czech　Academy　of　Sciences　2024.