A Poincaré-Birkhoff-Witt theorem for the quantum group of type \(A_ n\)

DOI10.3792/pjaa.64.385zbMath0677.17011OpenAlexW2016284972MaRDI QIDQ1123252

Hiroyuki Yamane

Publication date: 1988

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.pja/1195513062

zbMATH Keywords

quantum groupsHopf algebratriangular decomposition\(q\)-deformation of enveloping algebrasanalogue of Poincaré-Birkhoff-Witt theoremexplicit linear basis

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) General mathematical topics and methods in quantum theory (81Q99)

Related Items

UNIVERSAL ENVELOPING ALGEBRAS OF PBW TYPE, Unnamed Item

Cites Work

• Unnamed Item
• Infinite dimensional Lie algebras. An introduction
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Quantum deformations of certain simple modules over enveloping algebras
• Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra