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A Poincaré-Birkhoff-Witt theorem for the quantum group of type \(A_ n\). (English) Zbl 0677.17011
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 \(q(q^ 8-1)\neq 0\).

MSC:
17B35 Universal enveloping (super)algebras
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
81Q99 General mathematical topics and methods in quantum theory
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References:
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