A Poincaré-Birkhoff-Witt theorem for the quantum group of type \(A_ n\). (English) Zbl 0677.17011

Yamane, Hiroyuki

Proc. Japan Acad., Ser. A 64, No. 10, 385-386 (1988).

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 \(q(q^ 8-1)\neq 0\).

Reviewer: H. Boseck (Greifswald)

MSC:

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

Keywords:

quantum groups; \(q\)-deformation of enveloping algebras; Hopf algebra; explicit linear basis; analogue of Poincaré-Birkhoff-Witt theorem; triangular decomposition

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