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arXiv · 1609.03678

Ringel-Hall algebras beyond their quantum groups I: Restriction functor and Green's formula

Jie Xiao·Fan Xu·Minghui Zhao
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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.

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BibTeXRIS

Jie Xiao, Fan Xu, Minghui Zhao. 2016-09-13. Ringel-Hall algebras beyond their quantum groups I: Restriction functor and Green's formula. https://arxiv.org/abs/1609.03678

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