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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

ON SPECIALITY OF BINARY-LIE ALGEBRAS

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Author(s):
Arenas, Manuel [1] ; Shestakov, Ivan [2]
Total Authors: 2
Affiliation:
[1] Univ Chile, Fac Ciencias, Dept Matemat, Santiago - Chile
[2] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo - Brazil
Total Affiliations: 2
Document type: Journal article
Source: JOURNAL OF ALGEBRA AND ITS APPLICATIONS; v. 10, n. 2, p. 257-268, APR 2011.
Web of Science Citations: 0
Abstract

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)

FAPESP's process: 07/58048-8 - Binary-Lie algebras
Grantee:Manuel Camilo Arenas Carmona
Support Opportunities: Scholarships in Brazil - Post-Doctoral
FAPESP's process: 05/60337-2 - Lie and Jordan algebras, their representations and generalizations
Grantee:Ivan Chestakov
Support Opportunities: Research Projects - Thematic Grants