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

DOI10.1007/s10468-018-9821-5zbMath1472.16014arXiv1609.03678OpenAlexW2963224763WikidataQ129420379 ScholiaQ129420379MaRDI QIDQ2280108

Jie Xiao, Fan Xu, Ming Hui Zhao

Publication date: 17 December 2019

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.03678

zbMATH Keywords

Green formulaHall algebrainduction functorrestriction functorsimple perverse sheaf

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Representations of quivers and partially ordered sets (16G20)

Related Items (2)

Constructions of highest weight modules of double Ringel-Hall algebras via functions ⋮ The parity of Lusztig's restriction functor and Green's formula

Cites Work

• Quiver varieties and cluster algebras
• Hall algebras and quantum groups
• Equivariant sheaves and functors
• Lie algebras generated by indecomposables
• Drinfeld double and Ringel-Green theory of Hall algebras
• Hyperbolic localization of intersection cohomology
• Hall algebras, hereditary algebras and quantum groups
• Quiver varieties and Kac-Moody algebras
• Counting representations of quivers over finite fields
• Quantum Grothendieck rings and derived Hall algebras
• Graded quiver varieties, quantum cluster algebras and dual canonical basis
• Quivers with loops and perverse sheaves
• Quiver Hecke Algebras and 2-Lie Algebras
• Geometry and categorification
• Canonical bases and KLR-algebras
• Canonical Bases Arising from Quantized Enveloping Algebras
• A diagrammatic approach to categorification of quantum groups I
• Quivers, Perverse Sheaves, and Quantized Enveloping Algebras
• Lie algebras determined by finite auslander-reiten quivers
• Lectures on canonical and crystal bases of Hall algebras
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