On Lie algebras with primitive envelopes, supplements

Abstract

Let L be a finite dimensional Lie algebra over a field k of characteristic zero, U(L) its universal enveloping algebra and Z(D(L)) the center of the division ring of quotients of U(L).A number of conditions on L are each shown to be equivalent with the primitive of U(L).Also, a formula is given for the transcendency degree of Z(D(L)) over k.