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Lie bialgebras arising from alternative and Jordan bialgebras

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Abstract

We consider connection between simple alternative D-bialgebras and Lie bialgebras. We prove that each finite-dimensional alternative noncommutative algebra over an algebraically closed field may be equipped with the nontrivial structure of an alternative D-bialgebra.

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Authors and Affiliations

  1. Novosibirsk State University, Novosibirsk, Russia

    M. E. Goncharov

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  1. M. E. Goncharov
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Correspondence to M. E. Goncharov.

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Original Russian Text Copyright © 2010 Goncharov M. E.

The author was supported by the Russian Foundation for Basic Research (Grant 09-01-00157-a), the Russian Federal Agency for Education (Grant 2.1.1.419), the State Maintenance Program for the Leading Scientific Schools and the Young Scientists of the Russian Federation (Grants NSh-344.2008.1 and MD-2438.2009.1), the Integration Grant of the Siberian Division of the Russian Academy of Sciences (No. 97), and the Federal Target Program (No. 02.740.11.0429).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 2, pp. 268–284, March–April, 2010.

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Goncharov, M.E. Lie bialgebras arising from alternative and Jordan bialgebras. Sib Math J 51, 215–228 (2010). https://doi.org/10.1007/s11202-010-0022-7

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