La formule des hausteurs de tauvel dans les anneaux d'operateurs differentiels
Titel:
La formule des hausteurs de tauvel dans les anneaux d'operateurs differentiels
Auteur:
Guedenon, Thomas
Verschenen in:
Communications in algebra
Paginering:
Jaargang 21 (1993) nr. 6 pagina's 2077-2100
Jaar:
1993
Inhoud:
Throughout this paper, k is an algebraically closed field of chxacreriiric zero and R an associative algebra with identity over the field k. If U is the enveloping algebla of a finite dimenslonu1 rolvabie Lie algebia, then P. Tauvel [9] has shown that for eve])' prirne ideal P of U one has [image omitted] where htP denotes the height of the prime ideal P of U and d(U) denote the Gelfand-Krillov dimension of U over k. we call (*) Tauvel's height formula. Now, we fix an integers n and we form the differential operator rings [image omitted] defined as follows [image omitted] is the Ore extension of R by δ and for 2 ≤ i ≤ n the ring [image omitted] is the Ore extension of Ri-1 by δ1 All the δ1 are derivations of R and we set [image omitted] . We suppose that the two following conditions are always satisfied : (1) R is stable under the action of each δ1for (i=1,2,…,n). (2)Ri is stable under the action of each δj for 0≤i≤j≤n. If P is a δ1,n - invariant prime ideal of R we use δ1,n - htP to denote the δ1,n - height of P, that is, the supremum of the lengths of chain of δ1,n - invariant prime ideals of R with P at the top.
Tijdschrift beschrijving