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Varieties of dialgebras and conformal algebras

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Abstract

We introduce and study the concept of a variety of dialgebras which is closely related to the concept of a variety of conformal algebras: Each dialgebra of a given variety embeds into an appropriate conformal algebra of the same variety. In particular, the Leibniz algebras are exactly Lie dialgebras, and each Leibniz algebra embeds into a conformal Lie algebra.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    P. S. Kolesnikov

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  1. P. S. Kolesnikov
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Correspondence to P. S. Kolesnikov.

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Original Russian Text Copyright © 2008 Kolesnikov P. S.

The author was supported by the Russian Foundation for Basic Research and the Lavrent’ev Young Scientists Competition (No. 29).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 2, pp. 322–356, March–April, 2008.

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Kolesnikov, P.S. Varieties of dialgebras and conformal algebras. Sib Math J 49, 257–272 (2008). https://doi.org/10.1007/s11202-008-0026-8

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  • DOI: https://doi.org/10.1007/s11202-008-0026-8

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