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The centre of quantum sl_n at a root of unity

Rudolf Tange
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Abstract

It is proved that the centre Z of the simply connected quantised universal enveloping algebra over C, U_{\e,P}(sl_n), \e 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.

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Rudolf Tange. 2005-11-25. The centre of quantum sl_n at a root of unity. https://arxiv.org/abs/math/0511628

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