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Dialgebras and related triple systems

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Abstract

We consider some algebraical systems that lead to various nearly associative triple systems. We deal with a class of algebras which contains Leibniz-Poisson algebras, dialgebras, conformal algebras, and some triple systems. We describe all homogeneous structures of ternary Leibniz algebras on a dialgebra. For this purpose, in particular, we use the Leibniz-Poisson structure on a dialgebra. We then find a corollary describing the structure of a Lie triple system on an arbitrary dialgebra, a conformal associative algebra and a classical associative triple system. We also describe all homogeneous structures of an (ε, δ)-Freudenthal-Kantor triple system on a dialgebra.

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Author information

Correspondence to A. P. Pozhidaev.

Additional information

Original Russian Text Copyright © 2008 Pozhidaev A. P.

The author was supported by the Russian Foundation for Basic Research (Grant 05-01-00230) and the Siberian Division of the Russian Academy of Sciences (a grant No. 29 for the Junior Scientists and the Complex Integration Project 2006.1.9).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 4, pp. 870–885, July–August, 2008.

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Pozhidaev, A.P. Dialgebras and related triple systems. Sib Math J 49, 696–708 (2008). https://doi.org/10.1007/s11202-008-0067-z

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Keywords

  • dialgebra
  • ternary Leibniz algebra
  • Lie triple system
  • Freudenthal-Kantor triple system
  • enveloping algebra