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 A n .