On speciality of binary-Lie algebras
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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. © 2011 World Scientific Publishing Company.
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Artículo de publicación SCOPUS
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URI: https://repositorio.uchile.cl/handle/2250/153859
DOI: 10.1142/S0219498811004550
ISSN: 02194988
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Journal of Algebra and its Applications, Volumen 10, Issue 2, 2018, Pages 257-268
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