Exact structures and degeneration of Hall algebras

We study degenerations of the Hall algebras exact categories induced by degree functions on set isomorphism classes indecomposable objects. prove that each such degeneration algebra H(E) an category E is a smaller structure E′<E same additive A. When admissible in sense Enomoto, for any satisfying suitable finiteness conditions, we H(E′) this kind. In additively finite case, all form simplicial cone whose face lattice reflects properties structures. For representations Dynkin quivers, recover negative part corresponding quantum group, as well associated polyhedral studied Fourier, Reineke and first author. Along way, give minor improvements to certain results Enomoto Brüstle-Langford-Hassoun-Roy concerning classification structures category. idempotent complete A, there exists abelian Serre subcategories isomorphic show every Krull-Schmidt admits unique maximal Boolean.