Quantum groups and Hopf algebras

Lunedi' 18 Febbraio 2013 - Gaston Andres Garcia


Lunedi' 18 febbraio alle ore 15 in aula 1BC45 il Prof. Gaston Andres Garcia dell'Universita' di Cordoba (Argentina) terra' un seminario dal titolo "Quantum groups and Hopf algebras".

One of the main open problems in the theory of Hopf algebras is the classification of finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero. The first obstruction in solving the classification problem is the lack of examples. Hence, it is necessary to find new families of Hopf algebras. From the beginning, this role was played by quantum groups. These Hopf algebras, introduced in 1986 by Drinfeld, can be presented as deformations in one or more parameters of associative algebras related to semisimple (reductive) linear algebraic groups or semisimple (reductive) Lie algebras. They consists of a large family
with different structural properties and were used with profit to solve the classification problem for fixed dimensions.
After defining quantum groups and Hopf algebras, we will give some basic examples and we will study properties that characterize the known quantum groups. Finally, we will show how they get into the scene of the classification problem of pointed Hopf algebras with abelian coradical.

Rif. int. G. Carnovale