The double Ringel-Hall algebras of valued quivers.

DOI10.1007/s11401-005-0287-5zbMath1130.16013OpenAlexW1974483201MaRDI QIDQ2641570

Jie Xiao, Yanxin Wang

Publication date: 20 August 2007

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11401-005-0287-5

zbMATH Keywords

Kac-Moody algebrasquiversDrinfeld doublesRingel-Hall algebrasquantized enveloping algebrasirreducible highest weight modulesdimension vectors

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Representations of quivers and partially ordered sets (16G20)

Related Items (2)

Fourier transforms on Ringel-Hall algebras ⋮ The double Ringel-Hall algebra on a hereditary abelian finitary length category

Cites Work

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• Generalized Kac-Moody algebras
• Representations of K-species and bimodules
• Drinfeld double and Ringel-Green theory of Hall algebras
• Universal \(R\)-matrices and the center of the quantum generalized Kac-Moody algebras
• Universal PBW-bases of Hall-Ringel algebras and Hall polynomials
• A new approach to Kac's theorem on representations of valued quivers.
• On double Ringel-Hall algebras
• The Serre relations in Ringel-Hall algebras
• Hall algebras, hereditary algebras and quantum groups
• Quantum deformations of generalized Kac-Moody algebras and their modules
• Indecomposable representations of graphs and algebras
• Crystal bases for quantum generalized kac–moody algebras
• On the Iwahori-Matsumoto involution and applications
• Frobenius morphisms and representations of algebras
• A relation between a conjecture of Kac and the structure of the Hall algebra

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