The Rigid Dualizing Complex of a Universal Enveloping Algebra

仿射Hecke代数的刚性对偶复形

Rigid dualizing complexes of affine Hecke algebras

本文确定了约化根系关联的仿射Hecke代数$H_q$的刚性对偶复形，并推导出经典Hecke代数在特定条件下在其中心上为Frobenius的，且Nakayama自同构由显式对合给出。

Dualizing Complexes and Perverse Sheaves on Noncommutative Ringed Schemes

A quasi-coherent ringed scheme is a pair (X,A), where X is a scheme, and A is a noncommutative quasi-coherent O_X-ring. We introduce dualizing complexes over quasi-coherent ringed schemes and study their properties. For a separated differential quasi-coherent ringed scheme of finite type over a field, we prove existence and uniqueness of a rigid dualizing complex. In the proof we use the theory of perverse coherent sheaves in order to glue local pieces of the rigid dualizing complex into a global complex.

Dualizing Complexes and Perverse Modules over Differential Algebras

A differential algebra of finite type over a field k is a filtered algebra A, such that the associated graded algebra is finite over its center, and the center is a finitely generated k-algebra. The prototypical example is the algebra of differential operators on a smooth affine variety, when char k = 0. We study homological and geometric properties of differential algebras of finite type. The main results concern the rigid dualizing complex over such an algebra A: its existence, structure and variance properties. We also define and study perverse A-modules, and show how they are related to th…

关于经典李代数包络代数中诱导的完全素本原理想

On induced completely prime primitive ideals in enveloping algebras of classical Lie algebras

本文证明经典单李代数包络代数中的 Losev-Premet 理想均可由某个 Levi 子代数中关联簇为刚性幂零轨道闭包的 Losev-Premet 理想经抛物诱导得到，从而完成刚性 Losev-Premet 理想的分类。

Homological Transcendence Degree

Let D be a division algebra over a base field k. The homological transcendence degree of D, denoted by Htr D, is defined to be the injective dimension of the enveloping algebra of D. We show that Htr has several useful properties which the classical transcendence degree has. We extend some results of Resco, Rosenberg, Schofield and Stafford, and compute Htr for several classes of division algebras. The main tool for the computation is Van den Bergh's rigid dualizing complex.

Multiplicity-free primitive ideals associated with rigid nilpotent orbits

We prove that any finite W-algebra U(g,e) admits a one-dimensional representation fixed by the action of the component group of the centraliser of e. As a consequence, for any nilpotent orbit O in g there exists a multiplicity-free (and hence completely prime) primitive ideal of the universal enveloping algebra U(g) whose associated variety coincides with the Zariski closure of O.