Quantized coordinate rings, PBW-type bases and \(q\)-boson algebras

DOI10.1016/j.jalgebra.2016.01.007zbMath1397.17020arXiv1411.7824OpenAlexW2963473854MaRDI QIDQ5965125

Yoshihisa Saito

Publication date: 2 March 2016

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

Full work available at URL: https://arxiv.org/abs/1411.7824

zbMATH Keywords

quantum universal enveloping algebrasquantum coordinate rings

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Quantum groups (quantized function algebras) and their representations (20G42)

Related Items (2)

Representations of quantized coordinate algebras via PBW-type elements ⋮ Tetrahedron and 3D reflection equation from PBW bases of the nilpotent subalgebra of quantum superalgebras

Cites Work

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• Global crystal bases of quantum groups
• PBW basis of quantized universal enveloping algebras
• Algebra of functions on the quantum group SU(2)
• Modules over quantized coordinate algebras and PBW-bases
• A common structure in PBW bases of the nilpotent subalgebra of \(U_q(\mathfrak g)\) and quantized algebra of functions
• KILLING FORMS, HARISH-CHANDRA ISOMORPHISMS, AND UNIVERSAL R-MATRICES FOR QUANTUM ALGEBRAS
• Introduction to quantum groups

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