Generalization of nary Nambu algebras and beyond
(2009) In Journal of Mathematical Physics 50(8). Abstract
 The aim of this paper is to introduce nary Homalgebra structures generalizing the nary algebras of Lie type including nary Nambu algebras, nary NambuLie algebras and nary Lie algebras, and nary algebras of associative type including nary totally associative and nary partially associative algebras. We provide examples of the new structures and present some properties and construction theorems. We describe the general method allowing one to obtain an nary Homalgebra structure starting from an nary algebra and an nary algebra endomorphism. Several examples are derived using this process. Also we initiate investigation of classification problems for algebraic structures introduced in the article and describe all ternary... (More)
 The aim of this paper is to introduce nary Homalgebra structures generalizing the nary algebras of Lie type including nary Nambu algebras, nary NambuLie algebras and nary Lie algebras, and nary algebras of associative type including nary totally associative and nary partially associative algebras. We provide examples of the new structures and present some properties and construction theorems. We describe the general method allowing one to obtain an nary Homalgebra structure starting from an nary algebra and an nary algebra endomorphism. Several examples are derived using this process. Also we initiate investigation of classification problems for algebraic structures introduced in the article and describe all ternary threedimensional HomNambuLie structures with diagonal homomorphism. (C) 2009 American Institute of Physics. [DOI: 10.1063/1.3167801] (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1490682
 author
 Ataguema, H. ; Makhlouf, A. and Silvestrov, Sergei ^{LU}
 organization
 publishing date
 2009
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Journal of Mathematical Physics
 volume
 50
 issue
 8
 publisher
 American Institute of Physics (AIP)
 external identifiers

 wos:000269885700023
 scopus:69749097359
 ISSN
 00222488
 DOI
 10.1063/1.3167801
 language
 English
 LU publication?
 yes
 id
 e5c9af900abe4b5c8034ed8fb3727479 (old id 1490682)
 date added to LUP
 20160401 14:56:49
 date last changed
 20211006 01:30:02
@article{e5c9af900abe4b5c8034ed8fb3727479, abstract = {The aim of this paper is to introduce nary Homalgebra structures generalizing the nary algebras of Lie type including nary Nambu algebras, nary NambuLie algebras and nary Lie algebras, and nary algebras of associative type including nary totally associative and nary partially associative algebras. We provide examples of the new structures and present some properties and construction theorems. We describe the general method allowing one to obtain an nary Homalgebra structure starting from an nary algebra and an nary algebra endomorphism. Several examples are derived using this process. Also we initiate investigation of classification problems for algebraic structures introduced in the article and describe all ternary threedimensional HomNambuLie structures with diagonal homomorphism. (C) 2009 American Institute of Physics. [DOI: 10.1063/1.3167801]}, author = {Ataguema, H. and Makhlouf, A. and Silvestrov, Sergei}, issn = {00222488}, language = {eng}, number = {8}, publisher = {American Institute of Physics (AIP)}, series = {Journal of Mathematical Physics}, title = {Generalization of nary Nambu algebras and beyond}, url = {http://dx.doi.org/10.1063/1.3167801}, doi = {10.1063/1.3167801}, volume = {50}, year = {2009}, }