| 1. |
- Börjeson, Kaj, 1989-
(författare)
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A Algebras Derived from Associative Algebras with a Non-Derivation Differential
- 2015
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Ingår i: Journal of Generalized Lie Theory and Applications. - : OMICS Publishing Group. - 1736-5279 .- 1736-4337. ; 9:1
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Tidskriftsartikel (refereegranskat)abstract
- Given an associative graded algebra equipped with a degree +1 differential delta we define an A∞-structure that measures the failure of delta to be a derivation. This can be seen as a non-commutative analog of generalized BV-algebras. In that spirit we introduce a notion of associative order for the operator delta and prove that it satisfies properties similar to the commutative case. In particular when it has associative order 2 the new product is a strictly associative product of degree +1 and there is compatibility between the products, similar to ordinary BV-algebras. We consider several examples of structures obtained in this way. In particular we obtain an A∞-structure on the bar complex of an A∞-algebra that is strictly associative if the original algebra is strictly associative. We also introduce strictly associative degree +1 products for any degree +1 action on a graded algebra. Moreover, an A∞-structure is constructed on the Hochschild cocomplex of an associative algebra with a non-degenerate inner product by using Connes’ B-operator.
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| 2. |
- Palmkvist, Jakob, 1980-
(författare)
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A generalization of the Kantor-Koecher-Tits construction
- 2008
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Ingår i: Journal of Generalized Lie Theory and Applications. - : Tallinn University of Technology. - 1736-5279 .- 1736-4337. ; 2:3, s. 226-230
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Tidskriftsartikel (refereegranskat)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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| 3. |
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| 4. |
- 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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| 5. |
- Lundström, Patrik, 1971-
(författare)
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Weak topological functors
- 2008
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Ingår i: Journal of Generalized Lie Theory and Applications. - 1736-5279 .- 1736-4337. ; 2:3, s. 211-215
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Tidskriftsartikel (refereegranskat)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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| 6. |
- Makhlouf, Abdenacer, et al.
(författare)
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Hom-algebra structures
- 2008
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Ingår i: Journal of Generalized Lie Theory and Applications. - 1736-5279 .- 1736-4337. ; 2:2, s. 51-64
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Tidskriftsartikel (refereegranskat)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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| 7. |
- Porten, Egmont
(författare)
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Local envelopes on CR manifolds
- 2008
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Ingår i: Journal of Generalized Lie Theory and Applications. - 1736-5279 .- 1736-4337. ; 2, s. 240-244
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Tidskriftsartikel (refereegranskat)
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| 8. |
- Richter, Johan, et al.
(författare)
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On algebraic curves for commuting elements in $q$-Heisenberg algebras
- 2009
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Ingår i: Journal of Generalized Lie Theory and Applications. - 1736-5279 .- 1736-4337. ; 3:4, s. 321-328
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Tidskriftsartikel (refereegranskat)abstract
- In the present article we continue investigating the algebraic dependence of commuting elements in q-deformed Heisenberg algebras. We provide a simple proof that the 0-chain subalgebra is a maximal commutative subalgebra when q is of free type and that it coincides with the centralizer (commutant) of any one of its elements dierent from the scalar multiples of the unity. We review the Burchnall-Chaundy-type construction for proving algebraic dependence and obtaining corresponding algebraic curves for commuting elements in the q-deformed Heisenberg algebra by computing a certain determinant with entries depending on two commuting variables and one of the generators. The coe cients in front of the powers of the generator in the expansion of the determinant are polynomials in the two variables dening some algebraic curves and annihilating the two commuting elements. We show that for the elements from the 0-chain subalgebra exactly one algebraic curve arises in the expansion of the determinant. Finally, we present several examples of computation of such algebraic curves and also make some observations on the properties of these curves.
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| 9. |
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| 10. |
- 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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