Gröbner-Shirshov Basis of Quantum Groups

DOI10.1142/S1005386715000449zbMath1394.17041MaRDI QIDQ2949744

Zhenzhen Gao, Abdukadir Obul, Gulshadam Yunus

Publication date: 2 October 2015

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

zbMATH Keywords

Ringel-Hall algebraGröbner-Shirshov basisindecomposable module

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) Gröbner-Shirshov bases in nonassociative algebras (17A61)

Related Items (2)

Unnamed Item ⋮ Gröbner–Shirshov bases and their calculation

Cites Work

• Gröbner-Shirshov bases for quantum enveloping algebras
• Gröbner-Shirshov basis of quantum group of type \(\mathbb D_4\)
• A Poincaré-Birkhoff-Witt theorem for quantized universal enveloping algebras of type \(A_ N\)
• 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
• Gröbner-Shirshov basis of quantum group of type \(\mathbb E_6\)

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