Seminario de Teoría de Números

Some developments in hopf-Galois theory

Ponente: Marta Salguero García (Universitad de Barcelona)

Fecha: Lunes, 5 de febrero de 2018 – 13:30 h

Lugar: Aula 420, Módulo 17, Departamento de Matemáticas, UAM (Campus de Cantoblanco, Madrid)

Organiza: ICMAT-UAM

Resumen: Hopf-Galois theory is a generalization of Galois theory. The point is to replace Galois groups with Hopf algebras and the Galois action with a 'Hopf action' by endomorphisms. This pair gives the so-called Hopf-Galois structures. In this talk we will construct Hopf algebras and explain the general Hopf-Galois theory. We will focus on the case of separable extensions, in which there is a characterization in terms of groups. This allowed us to use Magma in order to explicitly obtain all of the possible Hopf-Galois structures of a given separable extension and to determine some important properties. We will describe the algorithms we designed and we will present the computational and theoretical results that we can derive from the collected data. This is the result of joint works with Teresa Crespo (UB).