论文标题
量子nilpotent代数
Catenarity in quantum nilpotent algebras
论文作者
论文摘要
在本文中，确定量子nilpotent代数（也称为CGL扩展）都是链纳级，即，在任何两个给定的素数$ p \ subsetneq q $之间，所有质量理想的含有的所有饱和链具有相同的长度。这是通过证明这些代数的主要光谱正常分离来实现的，然后建立了应用Lenagan和第一作者所必需的轻度同源条件。这项工作还恢复了量子nilpotent代数的Tauvel高度公式，这是Lenagan和作者通过不同的方法首先获得的。
In this paper, it is established that quantum nilpotent algebras (also known as CGL extensions) are catenary, i.e., all saturated chains of inclusions of prime ideals between any two given prime ideals $P \subsetneq Q$ have the same length. This is achieved by proving that the prime spectra of these algebras have normal separation, and then establishing the mild homological conditions necessary to apply a result of Lenagan and the first author. The work also recovers the Tauvel height formula for quantum nilpotent algebras, a result that was first obtained by Lenagan and the authors through a different approach.
