Construction of nLie algebras and nary HomNambuLie algebras
(2011) In Journal of Mathematical Physics 52(12). Abstract
 As nary 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. HomNambuLie algebras provide a framework that might be an appropriate setting in which nLie algebras (nary NambuLie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)ary HomNambuLie algebras from nary HomNambuLie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary... (More)
 As nary 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. HomNambuLie algebras provide a framework that might be an appropriate setting in which nLie algebras (nary NambuLie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)ary HomNambuLie algebras from nary HomNambuLie 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 nLie algebras and a kform satisfying certain conditions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3653197] (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2345079
 author
 Arnlind, Joakim ; Makhlouf, Abdenacer and Silvestrov, Sergei ^{LU}
 organization
 publishing date
 2011
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Journal of Mathematical Physics
 volume
 52
 issue
 12
 article number
 123502
 publisher
 American Institute of Physics (AIP)
 external identifiers

 wos:000298641000020
 scopus:84855279256
 ISSN
 00222488
 DOI
 10.1063/1.3653197
 language
 English
 LU publication?
 yes
 id
 4518bdf497f4487aaf967bb1a4520be6 (old id 2345079)
 date added to LUP
 20160401 13:59:35
 date last changed
 20210901 01:27:06
@article{4518bdf497f4487aaf967bb1a4520be6, abstract = {As nary 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. HomNambuLie algebras provide a framework that might be an appropriate setting in which nLie algebras (nary NambuLie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)ary HomNambuLie algebras from nary HomNambuLie 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 nLie algebras and a kform satisfying certain conditions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3653197]}, author = {Arnlind, Joakim and Makhlouf, Abdenacer and Silvestrov, Sergei}, issn = {00222488}, language = {eng}, number = {12}, publisher = {American Institute of Physics (AIP)}, series = {Journal of Mathematical Physics}, title = {Construction of nLie algebras and nary HomNambuLie algebras}, url = {http://dx.doi.org/10.1063/1.3653197}, doi = {10.1063/1.3653197}, volume = {52}, year = {2011}, }