Manuel Arenas
Universidad de Chile, Santiago, Chile
Įlgebras de Lie-Binįrias.
Abstract: The objective of the present work is to study the structure of Binary-Lie algebras, i.e. algebras where every pair of elements generates a Lie algebra. It is known that every Malcev algebra is Binary-Lie. We will study the relation of BL-algebras with assocyclic algebras (also called semialternative algebras) those are the algebras that satisfy the identity (ab)c-a(bc) = (bc)a-b(ca). If the original product of an assocyclic algebra is replaced by the Lie product ([a, b] = ab - ba) a Binary-Lie algebras is obtained as a result. We are interested in to find out whether every Binary-Lie algebra can be obtained by this process. This result would be a generalization of the well known Poincar“e-Birkhoff-Witt theorem. We plan also to start with the study of finite dimesional Binary-Lie superalgebras.