Gröbner-Shirshov basis for degenerate Ringel-Hall algebras of type \(F_4\)

DOI10.1007/S11401-016-1011-3zbMath1360.17016OpenAlexW2412737343MaRDI QIDQ266183

Abdukadir Obul, Zhenzhen Gao

Publication date: 13 April 2016

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

Full work available at URL: https://doi.org/10.1007/s11401-016-1011-3

zbMATH Keywords

Frobenius mapGröbner-Shirshov basisdegenerate Ringel-Hall algebrasmultiplication formulas

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Representations of quivers and partially ordered sets (16G20)

Cites Work

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• The diamond lemma for ring theory
• On algebras of finite representation type
• Embeddings into simple associative algebras
• On degenerations and extensions of finite dimensional modules
• Presenting degenerate Ringel-Hall algebras of type \(B\)
• Skew-commutator relations and Gröbner-Shirshov basis of quantum group of type \(F_4\)
• Generic extensions and multiplicative bases of quantum groups at 𝐪=0
• Indecomposable representations of graphs and algebras
• The Composition Algebra of a Cyclic Quiver
• Generic Extensions and Canonical Bases for Cyclic Quivers
• Frobenius morphisms and representations of algebras

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