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1.	Sigurdsson, Gunnar, et al. (author) Lie Color and Hom-Lie Algebras of Witt Type and Their Central Extensions 2009 In: GENERALIZED LIE THEORY IN MATHEMATICS, PHYSICS AND BEYOND. - BERLIN : SPRINGER-VERLAG BERLIN. - 9783540853312 - 9783540853329 ; , s. 247-255 Conference paper (peer-reviewed)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.
2.	Sigurdsson, Gunnar, et al. (author) Matrix bosonic realizations of a Lie colour algebra with three generators and five relations of Heisenberg Lie type 2009 In: Journal of Generalized Lie Theory and Applications. - 1736-5279 .- 1736-4337. ; 3:4, s. 329-340 Journal article (peer-reviewed)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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Author/Editor: Sigurdsson, Gunnar (2); Silvestrov, S. D., 1 ... (1); Silvestrov, Sergei (1)

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