On n-ary Lie Algebras of Type (r, l)

Reference : On n-ary Lie Algebras of Type (r, l)


	Document type :	Scientific congresses, symposiums and conference proceedings : Paper published in a book
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/26300

Title :	On n-ary Lie Algebras of Type (r, l)
Language :	English
Author, co-author :	Vishnyakova, Elizaveta [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Publication date :	2015
Main document title :	Geometric Methods in Physics
Editor :	Kielanowski, Piotr
	Bieliavsky, Pierre
	Odzijewicz, Anatol
	Schlichenmaier, Martin
	Voronov, Theodore
Publisher :	Birkhäuser
Collection and collection volume :	Trends in Mathematics
Pages :	227-234
Peer reviewed :	No
ISBN :	978-3-319-18211-7
Event name :	XXXIII Workshop
Event date :	June 29 – July 5, 2014
Event place (city) :	Białowieża
Event country :	Poland
Keywords :	[en] n-ary Lie algebras ; Nijenhuis–Richardson bracket ; Poisson bracket
Abstract :	[en] These notes are devoted to the multiple generalization of a Lie algebra introduced by A.M. Vinogradov and M.M. Vinogradov. We compare definitions of such algebras in the usual and invariant case. Furthermore, we show that there are no simple n-ary Lie algebras of type (n - 1, l) for l > 0.
Permalink :	http://hdl.handle.net/10993/26300
DOI :	10.1007/978-3-319-18212-4_17
Other URL :	http://arxiv.org/abs/1509.04050

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