活动地点：CMS 203

活动类型：学术报告

主讲人：Xingting Wang

活动时间：2016-06-17 15:30:00--2016-06-17 16:30:00

活动内容：

Title: PRIMITIVE DEFORMATION AND CLASSIFICATION OF HOPF ALGEBRAS UP TO PRIME-CUBE DIMENSION

Speaker: Xingting Wang (Temple University)

Time: June 17, 2016,  3:30-4:30pm

Place: CMS 203

Abstract

Finite dimensional Hopf algebras are special Frobenious algebras and also recoganized as nite quantum groups. The theory of quantum groups has strong connections with knot theory and low dimensional topology. These links come from their finite representations, which are tensor categories. The classication of nite-dimensional Hopf algebras in characteristic zero has been prosperous over the decades. In this talk, we discuss the problem of classifying nite-dimensional Hopf algebras in positive characteristic. These Hopf algebras are closely related to ane algebraic groups, restricted Lie algebras and p-groups theory.

A structured technique called primitive deformation is introduced and applied in the study of the isomorphism classes of nite-dimensional Hopf algebras in positive characteristic that are connected and satisfy certain restriction on their primitive spaces. As an application, we completely classify connected Hopf algebras of dimension up to p^3, where prime p is the characteristic of the base eld. Consequently, we provide new examples of Hopf algebras that are in (innite) parametric families. The associated quiver algebras, cohomology rings, and nite representation tensor category of these Hopf algebras are of broader interest and require thorough investigation. This is a joint work with Van Nguyen and Linhong Wang.