A Poincaré-Birkhoff-Witt theorem for the quantum group of type \(A_ n\)
The author describes a linear basis for the \(q\)-analogue \(U_ q(G)\) of the universal enveloping algebra in case \(G={\mathfrak sl}_{N+1}({\mathbb C})\). It follows, that \(U_ q({\mathfrak sl}_{N+1}({\mathbb C}))\) is a left (right) Noetherian ring without zero divisors provided \(q(q^ 8-1)\neq 0\).
\(q\)-deformation of enveloping algebras
analogue of Poincaré-Birkhoff-Witt theorem
scientific article; zbMATH DE number 4108965