arXiv subjects
Publications and source records attributed to Rudolf Tange.
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.
Let g be a Lie algebra over an algebraically closed field of characteristic p>0 and let U(g) be the universal enveloping algebra of g. We prove in this paper that for g=gl_n and g=sl_n the centre of U(g) is a unique factorisation domain and its field of fractions is rational. For g=sl_n our argument requires the assumption that p\nmid n while for g=gl_n it works for any p. It turned out that our two main results are closely related to each other. The first one confirms in type ${\rm A}$ a recent conjecture of A.Braun and C.Hajarnavis while the second answers a question of J.Alev.