On double Ringel-Hall algebras

DOI10.1006/jabr.2001.9151zbMath1010.16011OpenAlexW2055435624MaRDI QIDQ1614646

Bangming Deng, Jie Xiao

Publication date: 8 September 2002

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.2001.9151

zbMATH Keywords

Hopf algebrasKac-Moody algebrastensor productsquantum Yang-Baxter equationintegrable modulesDrinfeld doubles\(R\)-matrixRingel-Hall algebrasquantized enveloping algebrashighest weight categoriesfinite-dimensional hereditary algebrasKac-Weyl character formulacomposition subalgebrasirreducible integrable highest weight modulestorus algebras

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Finite rings and finite-dimensional associative algebras (16P10) Representations of quivers and partially ordered sets (16G20) Representations of associative Artinian rings (16G10)

Related Items (14)

Generalized Kac–Moody Lie Algebras and Product Quivers ⋮ The Coradical Filtration for Drinfeld Double Ringel-Hall Algebras ⋮ The double Ringel-Hall algebras of valued quivers. ⋮ Skew differential operator algebras of twisted Hopf algebras. ⋮ Refined geometric realization of a quantum group and Lusztig’s symmetries ⋮ BGP-reflection functors and Lusztig's symmetries of modified quantized enveloping algebras ⋮ Constructions of highest weight modules of double Ringel-Hall algebras via functions ⋮ Fourier transforms on Ringel-Hall algebras ⋮ Hall algebras of cyclic quivers and \(q\)-deformed Fock spaces ⋮ The double Ringel-Hall algebra on a hereditary abelian finitary length category ⋮ A realization of quantum groups via product valued quivers ⋮ Cyclic complexes, Hall polynomials and simple Lie algebras. ⋮ Fourier transforms and Ringel–Hall algebras of valued quivers ⋮ Ringel-Hall algebras and Lusztig's symmetries

Cites Work

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• Generalized Kac-Moody algebras
• Hall algebras and quantum groups
• Drinfeld double and Ringel-Green theory of Hall algebras
• Universal PBW-bases of Hall-Ringel algebras and Hall polynomials
• On the double of the Hall algebra of a quiver
• Ringel-Hall algebras and Lusztig's symmetries
• On Ringel-Hall algebras of tame hereditary algebras
• Hall algebras, hereditary algebras and quantum groups
• Canonical Bases Arising from Quantized Enveloping Algebras
• Indecomposable representations of graphs and algebras
• Representations of quivers over finite fields
• Introduction to quantum groups
• A relation between a conjecture of Kac and the structure of the Hall algebra
• BGP-reflection functors and Lusztig's symmetries: a Ringel-Hall algebra approach to quantum groups

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