Binary Lie álgebras

Resumo

The objective of the present work is to study the structure of Binary-Lie algebras i.e. algebras in which every pair of elements generates a Lie algebra. We study the relation between these algebras and Malcev algebras. It is known that every Malcev algebra is Binary-Lie. We also study its relation with assocyclic algebras (also called semialternative), those are algebras that satisfy the identity (ab)c-a(bc)= (bc)a-b(ca). If the original product of an associclyc algebra is replaced by the Lie product [a,b]= ab-ba, a Binary-Lie algebra is obtained as a result. We are interested in to find out if every Binary-Lie algebra can be embedded in another one obtained by this process. This result would be a generalization of Poincaré-Birkhoff-Witt theorem. We also plan to study the structure of Binary-Lie superalgebras of finite dimension. (AU)