Degenerate versions of Green's theorem for Hall modules

Green's theorem states that the Hall algebra of category representations a quiver over finite field is twisted bialgebra. Considering instead categories orthogonal or symplectic leads to class modules algebra, called modules, which are also comodules. A module theoretic analogue theorem, describing compatibility and comodule structures, not known. In this paper we prove analogues in degenerate settings finitary Rep F 1 ( Q ) constructible C . The result structures satisfy condition reminiscent Yetter–Drinfeld module.