A common structure in PBW bases of the nilpotent subalgebra of \(U_q(\mathfrak g)\) and quantized algebra of functions

DOI10.3842/SIGMA.2013.049zbMath1305.17013arXiv1302.6298MaRDI QIDQ2447818

Masato Okado, Yasuhiko Yamada, Atsuo Kuniba

Publication date: 29 April 2014

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.6298

zbMATH Keywords

quantized enveloping algebra tetrahedron equation quantized algebra of functions PBW bases

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) Applications of Lie algebras and superalgebras to integrable systems (17B80) Quantum groups (quantized function algebras) and their representations (20G42)

Related Items (9)

\(I\)-factorial quantum torsors and Heisenberg algebras of quantized universal enveloping type ⋮ Tetrahedron equation and quantum cluster algebras ⋮ Representations of quantized coordinate algebras via PBW-type elements ⋮ Integrable 3D lattice model in M-theory ⋮ Tetrahedron and 3D reflection equation from PBW bases of the nilpotent subalgebra of quantum superalgebras ⋮ Boundary from bulk integrability in three dimensions: 3D reflection maps from tetrahedron maps ⋮ Quantum flag manifolds as quotients of degenerate quantized universal enveloping algebras ⋮ Tetrahedron equation and quantum \(R\) matrices for \(q\)-oscillator representations of \(U_q(A^{(2)}_{2n})\), \(U_q(C^{(1)}_n)\) and \(U_q(D^{(2)}_{n+1})\) ⋮ Quantized coordinate rings, PBW-type bases and \(q\)-boson algebras

This page was built for publication: A common structure in PBW bases of the nilpotent subalgebra of \(U_q(\mathfrak g)\) and quantized algebra of functions