in technical terms means that ${\mathfrak{n}}$ admits a filtration by finite-dimensional subalgebras so that the centers of their enveloping algebras are appropriately aligned. This latter requirement singles out only one isomorphism class of subalgebras ${\mathfrak{n}}$. For such ${\mathfrak{n}}$ we construct a partial Dixmier map defined for certain linear forms $f\in{\mathfrak{n}}^*$, closely related to the Kostant cascade of ${\mathfrak{n}}$. We refer to these forms as Kostant forms. Our second main result (Theorem \[theo:ideal\_ifd\]) implies then that, similarly to the finite-dimensional case, the Dixmier map establishes a one-to-one correspondence between Kostant forms and centrally generated primitive ideals in $U({\mathfrak{n}})$. This provides an explicit description of the centrally generated primitive ideals of $U({\mathfrak{n}})$.

The paper is organized as follows. Section \[sect:finite\_dim\] is devoted to the finite-dimensional case. In Subsection \[sst:center\_fd\], we briefly recall the Kostant’s characterization of $Z({\mathfrak{n}})$ and present an explicit description of the canonical generators of $Z({\mathfrak{n}})$ from [@IgnatyevPenkov1 Subsection 2.1] based on A. Panov’s work [@Panov2]. (For the reader’s convenience, we present the answer for all classical Lie algebras ${\mathfrak{g}}$.) Subsection \[sst:ideals\_fd\] contains the proof of our first main result, Theorem \[theo:ideal\_fd\_Bn\_Dn\]. The key step in the proof is Proposition \[prop:J\_c\_primitive\_Bn\_Dn\]. We also find explicitly a set of “canonical” generators 