On Dixmier–Duflo isomorphism in positive characteristic – The classical nilpotent case

Let g be the nil radical of the Borel subalgebra of one of the classical simple Lie algebras over a field F of characteristic p⩾0. For p>0 we find an explicit realization of the center Z(g) of the enveloping algebra U(g) by generators and relations. This constructive approach yields an explicit isomorphism between Z(g) and the polynomial invariants algebra S(g)g. While realizing Z(g), we also prove that Z(g) is a complete intersection ring. Moreover, it leads to an explicit realization of Z(g) and S(g)g for p=0 as well. This extends a result of Dixmier in type An.