Non-associative algebras and bi-representation theory

This book is an introduction to the most important clases of non-associative algebras, namely Lie, Jordan and alternative algebras. It also presents the different definitions of representation and bi-representation, starting with the classic concept for groups and ending with Eilenberg definition for general non-associative algebras. It focuses in two issues that can be solved with this theory, the existence of an adjoint bi-representation and the existence of a faithful bi-representation. In order to solve this two problems it introduces the theory of free algebras and polynomial identities, together with its main results.

Autorentext

Manuel Arenas is a 42 years old mathematician. He works as an a professor of the Faculty of Sciences of the University of Chile since 2007. He studied between 1998 and 2005, year in which he obtained his PH.D. During 2009 he completed a post-doctorate at the University of Sao Paulo Brazil. His research field is non-associative algebra.