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Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras
Max Planck Institute for Gravitational Physics (AEI), Am Mühlenberg 1, D-14476 Golm, Germany.ORCID iD: 0000-0002-8727-2169
Université de Haute Alsace, Laboratoire de Mathématiques, Informatique et Applications, 4, rue des Frères Lumière F-68093 Mulhouse, France .
Mälardalen University, Division of Applied Mathematics, The School of Education, Culture and Communication, Box 883, 721 23 Västerås, Sweden och Centre for Mathematical Sciences, Lund University, Box 118, 221 00 Lund, Sweden .
2011 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 52, 123502Article in journal (Refereed) Published
Abstract [en]

As n-ary operations, generalizing Lie and Poisson algebras, arise in many different physical contexts, it is interesting to study general ways of constructing explicit realizations of such multilinear structures. Generically, they describe the dynamics of a physical system, and there is a need of understanding their quantization. Hom-Nambu-Lie algebras provide a framework that might be an appropriate setting in which n-Lie algebras (n-ary Nambu-Lie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)-ary Hom-Nambu-Lie algebras from n-ary Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n + k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions.

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2011. Vol. 52, 123502
National Category
Mathematics Mathematical Analysis Algebra and Logic
URN: urn:nbn:se:liu:diva-122351DOI: 10.1063/1.3653197OAI: diva2:865806
Available from: 2015-10-29 Created: 2015-10-29 Last updated: 2015-11-09

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Arnlind, Joakim
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