Gröbner-Shirshov basis of quantum group of type \(\mathbb D_4\)

DOI10.1007/s11401-011-0656-1zbMath1295.17015OpenAlexW2145240418MaRDI QIDQ741438

Abdukadir Obul, Gulshadam Yunus

Publication date: 12 September 2014

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

Full work available at URL: https://doi.org/10.1007/s11401-011-0656-1

zbMATH Keywords

indecomposable modulesRingel-Hall algebraGröbner-Shirshov basis

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15)

Related Items (8)

Gröbner-Shirshov bases of irreducible modules of the quantum group of type \(G_2\) ⋮ Gröbner-Shirshov basis for degenerate Ringel-Hall algebra of type \(D_4\) ⋮ Gröbner-Shirshov Basis of Quantum Groups ⋮ Gröbner-Shirshov basis of quantum group of type \(\mathbb E_6\) ⋮ Gröbner–Shirshov bases and their calculation ⋮ Skew-commutator relations and Gröbner-Shirshov basis of quantum group of type \(F_4\) ⋮ The skew-commutator relations and Gröbner-Shirshov bases of quantum group of type \(C_3\) ⋮ Gröbner-Shirshov bases of irreducible modules over the quantum group \(U_q(F_4)\)

Cites Work

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• Gröbner-Shirshov bases for quantum enveloping algebras
• A Poincaré-Birkhoff-Witt theorem for quantized universal enveloping algebras of type \(A_ N\)
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra
• Hall algebras and quantum groups
• The diamond lemma for ring theory
• Embeddings into simple associative algebras
• Unzerlegbare Darstellungen. I. (Indecomposable representations. I)
• PBW-bases of quantum groups.

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