Conference on Hopf Algebras and related topics

University Of Southern California, Los Angeles CA

Investigators

Abstract

ABSTRACT Principal Investigator: Guralnick, Robert M. Proposal Number: DMS - 0802098 Institution: University of Southern California Title: Conference on Hopf Algebras and related topics This award is to support a three day conference on Hopf Algebras and Related Topics be held on the campus of the Univeristy of Southern California during the period February 14 - 16, 2009. Hopf algebras are a common generalization of group algebras and Lie algebras. Many ideas from group theory and Lie theory are used to study Hopf algebras, but also Hopf algebras have been shown to be the right framework to study important problems in many areas. There have been recent advances in the subject with regard to classification problems, actions of Hopf algebras on rings, connections with noncommutative algebra, quantum groups, extensions to more general categories, invariant theory and representation theory of algebras. They have become an important tool in geometry and topology, especially knot theory, and provide a good framework for understanding invariants. They are used prominently in physics and chemistry. This conference will focus especially on certain aspects that have become increasingly important in recent years. There has been progress in classifying Hopf algebras and their representations, both in the pointed case (using some analogs of Lie methods) and in the semisimple case (with using more group-theoretic analogs). In particular the notion of Frobenius-Schur indicators, studied classically for finite groups and extended to Hopf algebras with a suitable definition, has become a major topic of investigation in Hopf algebras. Indicators have been used as a new invariant to classify Hopf algebras and to study the representations of Hopf algebras. In a different direction, there have been major advances about the stability of various radicals under actions of Hopf algebra, a classical problem. This conference will bring together experts in Hopf algebras, representation theory, ring theory and group theory with common interests in Hopf algebras but different viewpoints. It is expected that this will lead to even further advances and more connections among the different fields. A further goal of the conference is to expose outstanding postdoctoral and graduate students, especially women and other under represented groups, to the plethora of techniques and important problems in the area and to have them interact with some of the top people in the field.