Gröbner-Shirshov basis for degenerate Ringel-Hall algebra of type \(D_4\)

DOI10.1007/s12215-017-0321-yzbMath1401.16025OpenAlexW3170930188MaRDI QIDQ1632019

Rabigul Tuniyaz, Abdukadir Obul

Publication date: 12 December 2018

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12215-017-0321-y

zbMATH Keywords

presentationFrobenius mapGröbner-Shirshov basisdegenerate Ringel-Hall algebrasmultiplication formula

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Cohen-Macaulay modules in associative algebras (16G50) Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Quantum groups (quantized function algebras) and their representations (20G42) General theory of nonassociative rings and algebras (17A01)

Cites Work

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• Gröbner-Shirshov basis of quantum group of type \(\mathbb D_4\)
• The diamond lemma for ring theory
• Representations of K-species and bimodules
• Embeddings into simple associative algebras
• On degenerations and extensions of finite dimensional modules
• Presenting degenerate Ringel-Hall algebras of type \(B\)
• Generic extensions and multiplicative bases of quantum groups at 𝐪=0
• The Hall algebra and the composition monoid
• The Composition Algebra of a Cyclic Quiver
• Generic Extensions and Canonical Bases for Cyclic Quivers
• Frobenius morphisms and representations of algebras
• Feigin's map and monomial bases for quantized enveloping algebras

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