Ringel-Hall algebras beyond their quantum groups. I: Restriction functor and Green formula
type: Item
instance of: scholarly article
title: Ringel-Hall algebras beyond their quantum groups. I: Restriction functor and Green formula
zbMATH Open document ID: 1472.16014
author: Jie Xiao
author: Fan Xu
author: Minghui Zhao
published in: Algebras and Representation Theory
publication date: 2019-12-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/1609.03678
review text: 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.
reviewed by: Haicheng Zhang
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 7144055
zbMATH Keywords: Hall algebra
zbMATH Keywords: Green formula
zbMATH Keywords: induction functor
zbMATH Keywords: restriction functor
zbMATH Keywords: simple perverse sheaf
MaRDI profile type: Publication
OpenAlex ID: W2963224763
arXiv ID: 1609.03678
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Wikidata QID: Q129420379
DOI: 10.1007/S10468-018-9821-5
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description: scientific article