Abstract
Let g be a finite-dimensional Lie algebra over an algebraically closed field of characteristic p > 0 and let U ( g ) be the universal enveloping algebra of g . We show in this paper that the division ring of fractions of U ( g ) is isomorphic to the ring of fractions of a Weyl algebra in the following cases: for g = gl n or sl n if p ∤ n , for the Witt algebra W 1 and for some tensor product W 1 ⊗ A of W 1 with a truncated polynomial ring. Furthermore we also show that the centre of U ( g ) in the last two cases is a unique factorisation domain, in accordance with recent results of Premet, Tange, Braun and Hajarnavis.
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