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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

On $ (n+1)$-ary derivations of simple $ n$-ary Mal'tsev algebras


Author: I. B. Kaǐgorodov
Translated by: N. Lebedinskaya
Original publication: Algebra i Analiz, tom 25 (2013), nomer 4.
Journal: St. Petersburg Math. J. 25 (2014), 575-585
MSC (2010): Primary 17A36; Secondary 16W25
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.


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Additional 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

DOI: http://dx.doi.org/10.1090/S1061-0022-2014-01307-6
PII: S 1061-0022(2014)01307-6
Keywords: Ternary derivation, $(n+1)$-ary derivation, generalized derivation, Mal{\textprime}tsev algebra, binary-Lie algebra, ternary Mal{\textprime}tsev algebra
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)
Article copyright: © Copyright 2014 American Mathematical Society