# MathSciDoc: An Archive for Mathematician ∫

#### Quantum AlgebraRepresentation Theorymathscidoc:1610.29001

In this paper, we generalize the categorifical construction of a quantum group and its canonical basis by Lusztig (\cite{Lusztig,Lusztig2}) to the generic form of whole Ringel-Hall algebra. We clarify the explicit relation between the Green formula in \cite{Green} and the restriction functor in \cite{Lusztig2}. By a geometric way to prove Green formula, we show that the Hopf structure of a Ringel-Hall algebra can be categorified under Lusztig's framework.
Hall algebra, induction functor, restriction functor, simple perverse sheaves
```@inproceedings{jieringel-hall,