On $(n+1)$-ary derivations of simple $n$-ary Mal′tsev algebras
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I. B. Kaǐgorodov
Translated by: N. Lebedinskaya - St. Petersburg Math. J. 25 (2014), 575-585
- DOI: https://doi.org/10.1090/S1061-0022-2014-01307-6
- Published electronically: June 5, 2014
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Abstract:
The $(n+1)$-ary derivations of simple non-Lie $n$-ary Mal′tsev algebras are described in the case of the binary algebra $M_7$ and the ternary algebra $M_8$. As a consequence, a description is obtained for the $3$-ary derivations of simple non-Lie Mal′tsev algebras and simple finite-dimensional non-Lie binary-Lie algebras. Examples of semisimple Mal′tsev algebras having nontrivial $3$-ary derivations are given.References
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Bibliographic Information
- I. B. Kaǐgorodov
- Affiliation: S. L. Sobolev Mathematical Institute, Siberian Branch, Russian Academy of Sciences, Academic Koptyug ave. 4, Novosibirsk 630090, Russia; Instituto de Matematica e Estatistica, Universidade de Sao Paulo, Brazil
- Email: kaygorodov.ivan@gmail.com
- Received by editor(s): December 17, 2011
- Published electronically: June 5, 2014
- Additional Notes: Supported by RFBR (grants nos. 14-01-31084 and 14-01-31122), by the RF President Council an grants for young Russian scientists and scientific schools (project MK-330.2013.1), and by FAPESP (grant no. 2011/51132-9)
- © Copyright 2014 American Mathematical Society
- Journal: St. Petersburg Math. J. 25 (2014), 575-585
- MSC (2010): Primary 17A36; Secondary 16W25
- DOI: https://doi.org/10.1090/S1061-0022-2014-01307-6
- MathSciNet review: 3184617