The centre of quantum \(\mathfrak {sl}_n\) at a root of unity. (English) Zbl 1148.17011
J. Algebra 301, No. 1, 425-445 (2006); erratum 302, No. 2, 897-898 (2006).
Summary: It is proved that the centre \(Z\) of the simply connected quantised universal enveloping algebra over \(\mathbb {C},U_{\varepsilon,P}(\mathfrak {sl}_{n}), \varepsilon\) a primitive \(l\)th root of unity, \(l\) an odd integer \(>1\), has a rational field of fractions. Furthermore it is proved that if \(l\) is a power of an odd prime, \(Z\) is a unique factorisation domain.
MSC:
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
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