Topics on n-ary Algebraic Structures

Topics on n-ary Algebraic Structures

We review the basic definitions and properties of two types of n-ary structures, the Generalized Lie Algebras (GLA) and the Filippov (≡ n-Lie) algebras (FA), as well as those of their Poisson counterparts, the Generalized Poisson (GPS) and Nambu-Poisson (N-P) structures. We describe the Filippov alg...

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Main Authors: J. A. de Azcárraga, J. M. Izquierdo
Format: Article
Language:English
Published: CTU Central Library 2010-01-01
Series:Acta Polytechnica
Online Access:https://ojs.cvut.cz/ojs/index.php/ap/article/view/1179
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spelling doaj-2005873cdd7442ba8b63f40380606dc82020-11-24T20:57:43ZengCTU Central LibraryActa Polytechnica1210-27091805-23632010-01-015031179Topics on n-ary Algebraic StructuresJ. A. de AzcárragaJ. M. IzquierdoWe review the basic definitions and properties of two types of n-ary structures, the Generalized Lie Algebras (GLA) and the Filippov (≡ n-Lie) algebras (FA), as well as those of their Poisson counterparts, the Generalized Poisson (GPS) and Nambu-Poisson (N-P) structures. We describe the Filippov algebra cohomology complexes relevant for the central extensions and infinitesimal deformations of FAs. It is seen that semisimple FAs do not admit central extensions and, moreover, that they are rigid. This extends Whitehead’s lemma to all n ≥ 2, n = 2 being the original Lie algebra case. Some comments on<br />n-Leibniz algebras are also made.https://ojs.cvut.cz/ojs/index.php/ap/article/view/1179
collection DOAJ
language English
format Article
sources DOAJ
author J. A. de Azcárraga
J. M. Izquierdo
spellingShingle J. A. de Azcárraga
J. M. Izquierdo
Topics on n-ary Algebraic Structures
Acta Polytechnica
author_facet J. A. de Azcárraga
J. M. Izquierdo
author_sort J. A. de Azcárraga
title Topics on n-ary Algebraic Structures
title_short Topics on n-ary Algebraic Structures
title_full Topics on n-ary Algebraic Structures
title_fullStr Topics on n-ary Algebraic Structures
title_full_unstemmed Topics on n-ary Algebraic Structures
title_sort topics on n-ary algebraic structures
publisher CTU Central Library
series Acta Polytechnica
issn 1210-2709
1805-2363
publishDate 2010-01-01
description We review the basic definitions and properties of two types of n-ary structures, the Generalized Lie Algebras (GLA) and the Filippov (≡ n-Lie) algebras (FA), as well as those of their Poisson counterparts, the Generalized Poisson (GPS) and Nambu-Poisson (N-P) structures. We describe the Filippov algebra cohomology complexes relevant for the central extensions and infinitesimal deformations of FAs. It is seen that semisimple FAs do not admit central extensions and, moreover, that they are rigid. This extends Whitehead’s lemma to all n ≥ 2, n = 2 being the original Lie algebra case. Some comments on<br />n-Leibniz algebras are also made.
url https://ojs.cvut.cz/ojs/index.php/ap/article/view/1179
work_keys_str_mv AT jadeazcarraga topicsonnaryalgebraicstructures
AT jmizquierdo topicsonnaryalgebraicstructures
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