Binary-Lie algebras

• Grant number: 07/58048-8
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2008
• End date: February 28, 2009
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Ivan Chestakov
• Grantee: Manuel Camilo Arenas Carmona
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 05/60337-2 - Lie and Jordan algebras, their representations and generalizations, AP.TEM

Abstract

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)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

ARENAS, MANUEL; SHESTAKOV, IVAN. ON SPECIALITY OF BINARY-LIE ALGEBRAS. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, v. 10, n. 2, p. 257-268, APR 2011. (07/58048-8, 05/60337-2)