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Communications in Algebra Volume 38, 2010 - Issue 8
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Original Articles

Commutative n-Ary Leibniz Algebras

Pilar Benito Departamento de Matemáticas y Computación, Universidad de La Rioja, Logroño, Spain
,
S. Madariaga Departamento de Matemáticas y Computación, Universidad de La Rioja, Logroño, Spain
&
José M. Pérez-Izquierdo Departamento de Matemáticas y Computación, Universidad de La Rioja, Logroño, SpainCorrespondence[email protected]
Pages 2843-2850 | Received 27 Feb 2009, Published online: 18 Aug 2010
 
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Abstract

We prove that there are no simple commutative n-ary Leibniz algebras of arbitrary dimension over fields of characteristic zero or greater than n. This result extends previous work of Pojidaev and Elduque.

2000 Mathematics Subject Classification:

ACKNOWLEDGMENTS

The authors would like to thank Spanish Ministerio de Educación y Ciencia and FEDER MTM 2007-67884-C04-03 and the University of La Rioja. Sara Madariaga also thanks support from Spanish MICINN grant AP2007-01986 and ATUR 09/22.

Notes

Communicated by A. Elduque.

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