The center of the quotient division ring of the universal envelope of a Lie algebra

Abstract

Let L be a finite dimensional Lie algebra over a field k of characteristic zero, D(L) the quotient division ring of U(L). We compare the center Z(D(L)) with Z( D(H)) where H is an ideal of L of codimension one.

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.