A Proof of the Goodearl-Lenagan Polynormality Conjecture

作者：Yakimov Milen^*

来源：International Mathematics Research Notices, 2013, (9): 2097-2132.

DOI：10.1093/imrn/rns111

The quantum nilpotent algebras U_(w)(g), defined by De Concini-Kac-Procesi and Lusztig, are large classes of iterated skew polynomial rings with rich ring-theoretic structure. In this paper, we prove in an explicit way that all torus invariant prime ideals of the algebras U_(w)(g) are polynormal. In the special case of the algebras of quantum matrices, this construction yields explicit polynormal generating sets consisting of quantum minors for all of their torus invariant prime ideals. This gives a constructive proof of the Goodearl-Lenagan polynormality conjecture [15]. Furthermore, we prove that U_(w)(g) is normally separated for all simple Lie algebras g and Weyl group elements w, and deduce from it that all algebras U_(w)(g) are catenary.

• 出版日期2013