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  • 1. Larsson, Daniel
    et al.
    Sigurdsson, Gunnar
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Silvestrov, Sergei D.
    On some almost quadratic algebras coming from twisted derivations2006In: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, E-ISSN 1776-0852, Vol. 13, p. 76-86Article in journal (Refereed)
    Abstract [en]

    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.

  • 2.
    Sigurdsson, Gunnar
    KTH, Superseded Departments, Physics.
    Canoniical involutions and bosonic representations of three-dimensional lie colour algebras2004Licentiate thesis, comprehensive summary (Other scientific)
  • 3.
    Sigurdsson, Gunnar
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Silvestrov, Sergei
    Centre for Mathematical Sciences, Lund University.
    Lie Color and Hom-Lie Algebras of Witt Type and Their Central Extensions2009In: GENERALIZED LIE THEORY IN MATHEMATICS, PHYSICS AND BEYOND / [ed] Silvestrov S; Paal E; Abramov V; Stolin A, BERLIN: SPRINGER-VERLAG BERLIN , 2009, p. 247-255Conference paper (Refereed)
    Abstract [en]

    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.

  • 4.
    Sigurdsson, Gunnar
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Silvestrov, Sergei D.
    Bosonic realizations of the colour Heisenberg Lie algebra2006In: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, E-ISSN 1776-0852, Vol. 13, p. 110-128Article in journal (Refereed)
    Abstract [en]

    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.

  • 5.
    Sigurdsson, Gunnar
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Silvestrov, Sergei D.
    Graded quasi-Lie algebras of Witt type2006In: Czechoslovak Journal of Physics, ISSN 0011-4626, E-ISSN 1572-9486, Vol. 56, no 10-11, p. 1287-1291Article in journal (Refereed)
    Abstract [en]

    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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