Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras

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 un...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical physics 2011-12, Vol.52 (12), p.123502-123502-13
Main Authors: Arnlind, Joakim, Makhlouf, Abdenacer, Silvestrov, Sergei
Format: Article
Language:English
Subjects:
Algebra
Exact sciences and technology
General Mathematics
Hom-Lie algebra
Hom-Nambu-Lie algebra
Lie groups
Matematik
matematik/tillämpad matematik
Mathematical functions
Mathematical methods in physics
Mathematics
Mathematics/Applied Mathematics
Nambu-Lie algebra
Natural Sciences
Naturvetenskap
Physics
Sciences and techniques of general use
trace
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0022-2488
1089-7658
1089-7658
DOI:10.1063/1.3653197