| 1. |
- Ataguema, H., et al.
(författare)
-
Generalization of n-ary Nambu algebras and beyond
- 2009
-
Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 50:8, s. Article number 083501-
-
Tidskriftsartikel (refereegranskat)abstract
- The aim of this paper is to introduce n-ary Hom-algebra structures generalizing the n-ary algebras of Lie type including n-ary Nambu algebras, n-ary Nambu-Lie algebras and n-ary Lie algebras, and n-ary algebras of associative type including n-ary totally associative and n-ary 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 n-ary Hom-algebra structure starting from an n-ary algebra and an n-ary 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 three-dimensional Hom-Nambu-Lie structures with diagonal homomorphism.
|
|
| 2. |
|
|
| 3. |
- Sigurdsson, Gunnar, et al.
(författare)
-
Matrix bosonic realizations of a Lie colour algebra with three generators and five relations of Heisenberg Lie type
- 2009
-
Ingår i: Journal of Generalized Lie Theory and Applications. - 1736-5279 .- 1736-4337. ; 3:4, s. 329-340
-
Tidskriftsartikel (refereegranskat)abstract
- We describe realizations of a Lie colour algebra with three generators and five relations by matrices of power series in noncommuting indeterminates satisfying Heisenberg's canonical commutation relation of quantum mechanics. The obtained formulas are used to construct new operator representations of this Lie colour algebra using canonical representation of the Heisenberg commutation relation and creation and annihilation operators of the quantum mechanical harmonic oscillator.
|
|
