Localization in rings equipped with an action of a solvable Lie algebra
In [Compos. Math. 53, 347-367 (1984; Zbl 0561.16003)], the reviewer showed that the clique of a prime ideal of the enveloping algebra of a finite dimensional complex solvable Lie algebra \(\mathfrak g\) is localizable, and gave detailed results on the structure of the localized ring. Let \(R\) be a commutative Noetherian \(\mathbb{C}\)-algebra on which \(\mathfrak g\) acts as derivations, and set \(A=R\# U({\mathfrak g})\). Localizability of the cliques of \(A\) was proved by \textit{K. R. Goodearl} [J. Algebra 132, No. 1, 243-262 (1990; Zbl 0712.16017)]. The purpose of the article under review is to extend some of the structural results proved by the reviewer for the localizations of \(U({\mathfrak g})\) to the more general setting of \(R\# U({\mathfrak g})\). In particular, for the Ore set \(\mathcal T\) determined by a clique of \(A\), some sufficient conditions are given for the primitive ideals of \(A_{\mathcal T}\) to be generated by regular normalizing sequences.
finite dimensional complex solvable Lie algebras
scientific article; zbMATH DE number 1104104