The residual nilpotence of the multiplicative group of a skew field generated by universal enveloping algebras
Let L be a Lie algebra over a field k and U(L) its universal associative envelope. This algebra U(L) can be embedded in a skew field \(D=D(L)\) [cf. the reviewer, Proc. Lond. Math. Soc., III. Ser. 11, 511-530 (1961; Zbl 0104.032)]. The author's aim is a study of the multiplicative group \(D^*\); he proves here \(D^*\cong k^*\times D_ 1\) where the group \(D_ 1\) is either residually torsion-free nilpotent, when char k\(=0\), or a residually nilpotent p-group of bounded exponent when char k\(=p>0\). In the special case when L is soluble-by-finite dimensional, U(L) is an Ore domain and the assertion holds for its field of fractions.
scientific article; zbMATH DE number 4036011