Some Problems in Representation Theory and Algebraic Geometry

LUNTS 97-00964这个项目是研究量子群的局部化构造，重点是单位根的情况。它是与Alex Rosenberg合作项目的延续，该项目为通用案例构建了本地化。该项目的第二部分是研究Kodaira-Spencer李代数，它产生于代数簇的变形。这是最近与Eduard Looijenga一起开发的“镜像双重”图片。 量子群是最近从物理学中产生的代数对象。然而，这些对象的研究不仅有应用物理学也可以用来研究各种问题的一个纯粹的代数性质。

LUNTS 97-00964 This project is a study of the localization construction for quantum groups with emphasis on the roots of unity case. It is a continuation of the joint project with Alex Rosenberg where the localization was constructed for the generic case. The second part of the project is the study of the Kodaira-Spencer Lie algebra which arises in deformations of algebraic varieties. This is the "mirror dual" picture to the one developed recently with Eduard Looijenga. Quantum groups are algebraic objects which have recently arisen from physics. However, these objects whose study not only has applications to physics can also be used to study various questions of a purely algebraic nature.