| 1. |
- Larsson, Daniel, et al.
(författare)
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On some almost quadratic algebras coming from twisted derivations
- 2006
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Ingår i: Journal of Nonlinear Mathematical Physics. - 1402-9251 .- 1776-0852. ; 13, s. 76-86
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Tidskriftsartikel (refereegranskat)abstract
- This paper explores the quasi-deformation scheme devised in [1, 3] as applied to the simple Lie algebra sl(2)(F) for specific choices of the involved parameters and underlying algebras. 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 sl(2)(F) one obtains multiparameter families of almost quadratic algebras, and by choosing parameters suitably, sl(2)(F) is quasi-deformed into three-dimensional and four-dimensional Lie algebras and algebras closely resembling Lie superalgebras and colour Lie algebras, this being in stark contrast to the classical deformation schemes where sl(2)(F) is rigid.
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| 2. |
- Larsson, Daniel, et al.
(författare)
-
On some almost quadratic algebras coming from twisted derivations
- 2006
-
Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 13, s. 76-86
-
Tidskriftsartikel (refereegranskat)abstract
- This paper explores the quasi-deformation scheme devised in [1, 3] as applied to the simple Lie algebra sl(2)(F) for specific choices of the involved parameters and underlying algebras. 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 sl(2)(F) one obtains multiparameter families of almost quadratic algebras, and by choosing parameters suitably, sl(2)(F) is quasi-deformed into three-dimensional and four-dimensional Lie algebras and algebras closely resembling Lie superalgebras and colour Lie algebras, this being in stark contrast to the classical deformation schemes where sl(2)(F) is rigid.
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| 3. |
- Sigurdsson, Gunnar, et al.
(författare)
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Bosonic realizations of the colour Heisenberg Lie algebra
- 2006
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 13, s. 110-128
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Tidskriftsartikel (refereegranskat)abstract
- We describe realizations of the colour analogue of the Heisenberg Lie algebra by power series in non-commuting indeterminates satisfying Heisenberg's canonical commutation relations of quantum mechanics. The obtained formulas are used to construct new operator representations of the colour Heisenberg Lie algebra. These representations are shown to be closely connected with some combinatorial identities and functional difference-differential interpolation formulae involving Euler numbers.
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| 4. |
- Sigurdsson, Gunnar, et al.
(författare)
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Graded quasi-Lie algebras of Witt type
- 2006
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Ingår i: Czechoslovak Journal of Physics. - : Springer Science and Business Media LLC. - 0011-4626 .- 1572-9486. ; 56:10-11, s. 1287-1291
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Tidskriftsartikel (refereegranskat)abstract
- In this article, we introduce a new class of graded algebras called quasi-Lie algebras of Witt type. These algebras can be seen as a generalization of other Witt-type algebras like Lie algebras of Witt type and their colored version, Lie color algebras of Witt type.
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