ON SPECIALITY OF BINARY-LIE ALGEBRAS

Autor(es)

Arenas, Manuel ^[1] ; Shestakov, Ivan ^[2]

Afiliação do(s) autor(es)

^[1] Univ Chile, Fac Ciencias, Dept Matemat, Santiago - Chile

^[2] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF ALGEBRA AND ITS APPLICATIONS; v. 10, n. 2, p. 257-268, APR 2011.
• Citações Web of Science: 0

Resumo

In the present work, binary-Lie, assocyclic, and binary (-1,1) algebras are studied. We prove that, for every assocyclic algebra A, the algebra A(-) is binary-Lie. We find a simple non-Malcev binary-Lie superalgebra T that cannot be embedded in A(-s) for an assocyclic superalgebra A. We use the Grassmann envelope of T to prove the similar result for algebras. This solve negatively a problem by Filippov (see {[}1, Problem 2.108]). Finally, we prove that the superalgebra T is isomorphic to the commutator superalgebra A(-s) for a simple binary (-1,1) superalgebra A. (AU)

• Processo FAPESP: 07/58048-8 - Binary Lie álgebras
• Beneficiário: Manuel Camilo Arenas Carmona
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 05/60337-2 - Álgebras de Lie e de Jordan, suas representações e generalizações
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Temático