In　this　paper　we　study　the　category　Cm(P)　of　m-cyclic　complexes　over　P,　where　P　is　the　category　of　projective　modules　over　a　finite　dimensional　hereditary　algebra　A,　and　describe　almost　split　sequences　in　Cm(P).　This　is　applied　to　prove　the　existence　of　Hall　polynomials　in　Cm(P)　when　A　is　representation　finite　and　m≠.　1.　We　further　introduce　the　Hall　algebra　of　Cm(P)　and　its　localization　in　the　sense　of　Bridgeland.　In　the　case　when　A　is　representation　finite,　we　use　Hall　polynomials　to　define　the　generic　Bridgeland-Hall　algebra　of　A　and　show　that　it　contains　a　subalgebra　isomorphic　to　the　integral　form　of　the　corresponding　quantum　enveloping　algebra.　This　provides　a　construction　of　the　simple　Lie　algebra　associated　with　A.　©　2015　Elsevier　Inc.