论文标题
泊松痕迹
Poisson trace orders
论文作者
论文摘要
到目前为止，已经以完全独立的方式应用了对订单不可约说明的研究（通过痕迹和泊松订单）的两种主要方法。我们定义并研究两种方法之间的自然兼容性关系，从而导致泊松痕量订单的概念。事实证明，所有常规和减少的痕迹始终与任何泊松订单结构兼容。在自然假设（最大订单和开务-Hamilton代数）下，所有Poisson痕量订单的修改判别理想被证明是泊松理想，判别理想的零基因座被证明是符号核心的工会。证明了泊松痕量订单的基本变更定理。 A broad range of Poisson trace orders are constructed based on the proved theorems: quantized universal enveloping algebras, quantum Schubert cell algebras and quantum function algebras at roots of unity, symplectic reflection algebras, 3 and 4-dimensional Sklyanin algebras, Drinfeld doubles of pre-Nichols algebras of diagonal type, and root of unity quantum集群代数。
The two main approaches to the study of irreducible representations of orders (via traces and Poisson orders) have so far been applied in a completely independent fashion. We define and study a natural compatibility relation between the two approaches leading to the notion of Poisson trace orders. It is proved that all regular and reduced traces are always compatible with any Poisson order structure. The modified discriminant ideals of all Poisson trace orders are proved to be Poisson ideals and the zero loci of discriminant ideals are shown to be unions of symplectic cores, under natural assumptions (maximal orders and Cayley--Hamilton algebras). A base change theorem for Poisson trace orders is proved. A broad range of Poisson trace orders are constructed based on the proved theorems: quantized universal enveloping algebras, quantum Schubert cell algebras and quantum function algebras at roots of unity, symplectic reflection algebras, 3 and 4-dimensional Sklyanin algebras, Drinfeld doubles of pre-Nichols algebras of diagonal type, and root of unity quantum cluster algebras.
