| 1. |
- Palmkvist, Jakob, 1980-
(author)
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A generalization of the Kantor-Koecher-Tits construction
- 2008
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In: Journal of Generalized Lie Theory and Applications. - : Tallinn University of Technology. - 1736-5279 .- 1736-4337. ; 2:3, s. 226-230
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Journal article (peer-reviewed)abstract
- The Kantor-Koecher-Tits construction associates a Lie algebra to any Jordan algebra. We generalize this construction to include also extensions of the associated Lie algebra. In particular, the conformal realization of so(p + 1, q + 1) generalizes to so(p + n, q + n), for arbitrary n, with a linearly realized subalgebra so(p, q). We also show that the construction applied to 3 × 3 matrices over the division algebras R, C, H, O gives rise to the exceptional Lie algebras f4, e6, e7, e8, as well as to their affine, hyperbolic and further extensions.
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| 2. |
- Larsson, Daniel, et al.
(author)
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Quasi-Lie deformations on the algebra F[t]/(tn)
- 2008
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In: Journal of Generalized Lie Theory and Applications. - 1736-5279 .- 1736-4337. ; 2:3, s. 201-205
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Journal article (peer-reviewed)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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| 3. |
- Lundström, Patrik, 1971-
(author)
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Weak topological functors
- 2008
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In: Journal of Generalized Lie Theory and Applications. - 1736-5279 .- 1736-4337. ; 2:3, s. 211-215
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Journal article (peer-reviewed)abstract
- We introduce weak topological functors and show that they lift and preserve weak limits and weak colimits. We also show that if then the induced functor of Wyler’s top categories and in particular to functor categories of fuzzy maps, fuzzy relations, fuzzy topological spaces and fuzzy measurable spaces. A ! B is a topological functor and J is a category,AJ ! BJ is topological. These results are applied to a generalization
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| 4. |
- Makhlouf, Abdenacer, et al.
(author)
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Hom-algebra structures
- 2008
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In: Journal of Generalized Lie Theory and Applications. - 1736-5279 .- 1736-4337. ; 2:2, s. 51-64
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Journal article (peer-reviewed)abstract
- A Hom-algebra structure is a multiplication on a vector space where the structure is twisted by a homomorphism. The structure of Hom-Lie algebra was introduced by Hartwig, Larsson and Silvestrov in [4] and extended by Larsson and Silvestrov to quasi-hom Lie and quasi-Lie algebras in [5, 6]. In this paper we introduce and study Hom-associative, Hom-Leibniz, and Hom-Lie admissible algebraic structures which generalize the well known associative, Leibniz and Lie admissible algebras. Also, we characterize the flexible Hom-algebras in this case. We also explain some connections between Hom-Lie algebras and Santilli’s isotopies of associative and Lie algebras.
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| 5. |
- Porten, Egmont
(author)
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Local envelopes on CR manifolds
- 2008
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In: Journal of Generalized Lie Theory and Applications. - 1736-5279 .- 1736-4337. ; 2, s. 240-244
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Journal article (peer-reviewed)
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| 6. |
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| 7. |
- Öinert, Johan, et al.
(author)
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Commutativity and ideals in algebraic crossed products
- 2008
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In: Journal of Generalized Lie Theory and Applications. - 1736-5279 .- 1736-4337. ; 2:4, s. 287-302
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Journal article (peer-reviewed)abstract
- We investigate properties of commutative subrings and ideals in non-commutative algebraic crossed products for actions by arbitrary groups. A description of the commutant of the coefficient subring in the crossed product ring is given. Conditions for commutativity and maximal commutativity of the commutant of the coefficient subring are provided in terms of the action as well as in terms of the intersection of ideals in the crossed product ring with the coefficient subring, specially taking into account both the case of coefficient rings without non-trivial zero-divisors and the case of coefficient rings with non-trivial zero-divisors.
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| 8. |
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