| 1. |
- Larsson, Daniel, et al.
(författare)
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Quasi-Lie deformations on the algebra F[t]/(tn)
- 2008
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Ingår i: Journal of Generalized Lie Theory and Applications. - 1736-5279 .- 1736-4337. ; 2:3, s. 201-205
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Tidskriftsartikel (refereegranskat)abstract
- This paper explores the quasi-deformation scheme devised by Hartwig, Larsson and Silvestrov as applied to the simple Lie algebra sl2(F). One of the main points of this method is that the quasi-deformed algebra comes endowed with a canonical twisted Jacobi identity. We show in the present article that when the quasi-deformation method is applied to sl2(F) via representations by twisted derivations on the algebra F[t]/(tN) one obtains interesting new multi-parameter families of almost quadratic algebras.
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| 2. |
- Sigurdsson, Gunnar, et al.
(författare)
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Lie Color and Hom-Lie Algebras of Witt Type and Their Central Extensions
- 2009
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Ingår i: GENERALIZED LIE THEORY IN MATHEMATICS, PHYSICS AND BEYOND. - BERLIN : SPRINGER-VERLAG BERLIN. - 9783540853312 - 9783540853329 ; , s. 247-255
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Konferensbidrag (refereegranskat)abstract
- In this article, two classes of Gamma-graded Witt-type algebras, Lie color and hom-Lie algebras of Witt type, are considered. These algebras can be seen as generalizations of Lie algebras of Witt type. One-dimensional central extensions of Lie color and hom-Lie algebras of Witt type are investigated.
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| 3. |
- Sigurdsson, Gunnar, et al.
(författare)
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Matrix bosonic realizations of a Lie colour algebra with three generators and five relations of Heisenberg Lie type
- 2009
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Ingår i: Journal of Generalized Lie Theory and Applications. - 1736-5279 .- 1736-4337. ; 3:4, s. 329-340
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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.
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