Ringel-Hall algebras beyond their quantum groups. I: Restriction functor and Green formula
In the paper under review, the authors generalize the categorical construction of a quantum group and its canonical basis introduced by Lusztig to the generic form of the whole Ringel-Hall algebra. They clarify the explicit relation between the Green formula and the restriction functor. By a geometric way to prove the Green formula, they show that the compatibility of multiplication and comultiplication of a Ringel-Hall algebra can be categorified under Lusztig's framework.
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