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An analogue of P.B.W. theorem and the universal R-matrix for $$U_ h\mathfrak{sl}(N+1)$$. (English) Zbl 0694.17006
For the “quantum” deformation of $$\mathfrak{sl}(n;{\mathbb C})$$ the universal R-matrix, the measure of noncocommutativity of $$U_ h(\mathfrak{sl}(n;{\mathbb C}))$$, is explicitly calculated. For this the basis of the quantum deformation $$U_ h(\mathfrak{sl}(n;{\mathbb C}))$$ of the enveloping algebra – the P.B.W. theorem – is formulated.
Remark. The answer for the R-matrix might only by accident be true for $$h$$ such that $$h^ 8=1$$: in this case the P.B.W. theorem reads differently [cf. H. Yamane, Publ. Res. Inst. Math. Sci. 25, No. 3, 503–520 (1989; Zbl 0694.17007)].
Reviewer: D. Leites

##### MSC:
 17B37 Quantum groups (quantized enveloping algebras) and related deformations 16W30 Hopf algebras (associative rings and algebras) (MSC2000) 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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##### References:
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