\(\imath\) Hall algebras and \(\imath\) quantum groups

DOI10.1090/pspum/108/01967MaRDI QIDQ6629985

Ming Lu, Weiqiang Wang

Publication date: 30 October 2024

zbMATH Keywords

quantum groupsHall algebrasquantum symmetric pairs

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Differential graded algebras and applications (associative algebraic aspects) (16E45) Derived categories, triangulated categories (18G80)

Cites Work

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• Graded quiver varieties and derived categories
• Modulation and natural valued quiver of an algebra.
• Quantum symmetric Kac-Moody pairs
• Representations of quivers over the algebra of dual numbers
• Braid group actions on coideal subalgebras of quantized enveloping algebras
• The Hall algebra approach to Drinfeld's presentation of quantum loop algebras
• Geometric Schur duality of classical type
• Derived Hall algebras
• Hall algebras associated to triangulated categories
• Hall algebras and quantum groups
• Heisenberg doubles and derived categories
• Eisenstein series and quantum affine algebras
• Braid group action and quantum affine algebras
• Drinfeld double and Ringel-Green theory of Hall algebras
• Triangulated categories and Kac-Moody algebras
• Canonical bases arising from quantum symmetric pairs
• Modified Ringel-Hall algebras, Green's formula and derived Hall algebras
• Formulae of \(\iota\)-divided powers in \(\mathbf{U}_q(\mathfrak{sl}_2)\)
• Chain complexes and stable categories
• On the double of the Hall algebra of a quiver
• Symmetric pairs for quantized enveloping algebras
• Noncommutative projective curves and quantum loop algebras
• Hall algebras, hereditary algebras and quantum groups
• Quantum groups via Hall algebras of complexes.
• Relative homological algebra
• A Serre presentation for the \(\imath\)quantum groups
• Semi-derived Ringel-Hall algebras and Drinfeld double
• Singularity categories of Gorenstein monomial algebras
• Hall algebras and quantum symmetric pairs. III: Quiver varieties
• A Drinfeld type presentation of affine \(\imath\) quantum groups. I: Split ADE type
• A Drinfeld-type presentation of affine \(\imath\) quantum groups. II: Split BCFG type
• Braid group symmetries on quasi-split \(\imath\)quantum groups via \(\imath\)Hall algebras
• Serre-Lusztig relations for \({\iota}\) quantum groups. III
• Braid group action for the \(q\)-Onsager algebra
• The Happel functor and homologically well-graded Iwanaga-Gorenstein algebras
• Generalized quiver varieties and triangulated categories
• From the Drinfeld realization to the Drinfeld-Jimbo presentation of affine quantum algebras: injectivity
• Quivers with relations for symmetrizable Cartan matrices. I: Foundations
• Deformed universal characters for classical and affine algebras
• On triangulated orbit categories
• Exact categories
• Hall algebras and quantum symmetric pairs. II: Reflection functors
• Serre-Lusztig relations for \(\imath\) quantum groups
• Quantum groups via cyclic quiver varieties I
• The composition Hall algebra of a weighted projective line
• The elliptic Hall algebra, Cherednik Hecke algebras and Macdonald polynomials
• Quiver varieties and Hall algebras
• Sur La Classification Des Fibres Holomorphes Sur La Sphere de Riemann
• Positivity of Canonical Bases Under Comultiplication
• The bar involution for quantum symmetric pairs
• Canonical Bases Arising from Quantized Enveloping Algebras
• Deriving DG categories
• PBW-basis for the composition algebra of the Kronecker algebra
• Semi-Derived and Derived Hall Algebras for Stable Categories
• Hecke Algebras with Unequal Parameters
• PBW-bases of quantum groups.
• A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs
• Canonical bases arising from quantum symmetric pairs of Kac–Moody type
• Affine flag varieties and quantum symmetric pairs
• Giambelli, Pieri, and tableau formulas via raising operators
• 𝚤Hall algebra of the projective line and 𝑞-Onsager algebra
• Introduction to quantum groups
• BGP-reflection functors and Lusztig's symmetries: a Ringel-Hall algebra approach to quantum groups
• Braid group action and quasi-split affine 𝚤quantum groups I
• Relative braid group symmetries on \(\imath\)quantum groups of Kac-Moody type
• Hall algebras and quantum symmetric pairs I: Foundations
• Hall algebras and quantum symmetric pairs of Kac-Moody type
• An intrinsic approach to relative braid group symmetries on ı$\imath$quantum groups
• 𝚤Hall algebras of weighted projective lines and quantum symmetric pairs

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