Ringel-Hall algebras beyond their quantum groups I: Restriction functor and Green's formula
Representation Theory
2017-11-27 v3 Quantum Algebra
Abstract
In this paper, we generalize the categorifical construction of a quantum group and its canonical basis introduced by Lusztig (\cite{Lusztig,Lusztig2}) to the generic form of the 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 the Green formula, we show that the Hopf structure of a Ringel-Hall algebra can be categorified under Lusztig's framework.
Keywords
Cite
@article{arxiv.1609.03678,
title = {Ringel-Hall algebras beyond their quantum groups I: Restriction functor and Green's formula},
author = {Jie Xiao and Fan Xu and Minghui Zhao},
journal= {arXiv preprint arXiv:1609.03678},
year = {2017}
}
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30 pages