TWO DESCRIPTIONS OF THE QUANTUM AFFINE ALGEBRA Uv() VIA HALL ALGEBRA APPROACH

DOI10.1017/S0017089511000607zbMath1247.17010arXiv0903.4828MaRDI QIDQ2882493

Igor Burban, Olivier Schiffmann

Publication date: 6 May 2012

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.4828

zbMATH Keywords

derived categoryHall algebraaffine algebraquantum algebraDrinfeld doublecoherent sheafKronecker quiver

Mathematics Subject Classification ID

Related Items (8)

Essential dimension and genericity for quiver representations ⋮ 𝚤Hall algebras of weighted projective lines and quantum symmetric pairs ⋮ Quantum groups via Hall algebras of complexes. ⋮ Essential dimension of representations of algebras ⋮ Double Hall algebras and derived equivalences. ⋮ The Hall algebra approach to Drinfeld's presentation of quantum loop algebras ⋮ 𝚤Hall algebra of the projective line and 𝑞-Onsager algebra ⋮ Remarks on Hall algebras of triangulated categories

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Zur Homotopietheorie der Kettenkomplexe
• Hall numbers and the composition algebra of the Kronecker algebra.
• Double Hall algebras and derived equivalences.
• Coherent sheaves on \({\mathbb{P}}^n\) and problems of linear algebra
• Hall algebras and quantum groups
• Eisenstein series and quantum affine algebras
• Isomorphism of two realizations of quantum affine algebra \(U_ q(\widehat{\mathfrak{gl}}(n))\)
• Braid group action and quantum affine algebras
• Drinfeld double and Ringel-Green theory of Hall algebras
• Root categories and simple Lie algebras
• Stability for an abelian category
• The Harder-Narasimhan system in quantum groups and cohomology of quiver moduli
• On the double of the Hall algebra of a quiver
• Hall algebras, hereditary algebras and quantum groups
• An algebraic characterization of the affine canonical basis
• Stability conditions on triangulated categories
• Canonical bases and moduli spaces of sheaves on curves
• The Kronecker quiver and bases of quantum affine \(\mathfrak{sl}_2\)
• Noetherian hereditary abelian categories satisfying Serre duality
• BGP-reflection functors and Lusztig's symmetries: a Ringel-Hall algebra approach to quantum groups

This page was built for publication: TWO DESCRIPTIONS OF THE QUANTUM AFFINE ALGEBRA U_v() VIA HALL ALGEBRA APPROACH