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Журнал обобщенной теории лжи и ее приложений

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Объем 8, Проблема 1 (2014)

исследовательская статья

The Normal Ordering Procedure and Coherent State of the Q-Deformed Generalized Heisenberg Algebra

Won Sang Chung

In this paper we discuss the normal ordering procedure of the q-deformed generalized Heisenberg algebra. We also obtain the coherent state for some types of characteristic functions.

исследовательская статья

Modules Over Color Hom-Poisson Algebras

Ibrahima Bakayoko

In this paper we introduce color Hom-Poisson algebras and show that every color Hom-associative algebra has a non-commutative Hom-Poisson algebra structure in which the Hom-Poisson bracket is the commutator bracket. Then we show that color Poisson algebras (respectively morphism of color Poisson algebras) turn to color Hom-Poisson algebras (respectively morphism of Color Hom-Poisson algebras) by twisting the color Poisson structure. Next we prove that modules over color Hom–associative algebras A extend to modules over the color Hom-Lie algebras L(A), where L(A) is the color Hom-Lie algebra associated to the color Hom-associative algebra A. Moreover, by twisting a color Hom-Poisson module structure map by a color Hom-Poisson algebra endomorphism, we get another one.

Редакционный

Constructive Approach to Three Dimensional Sklyanin Algebras

Natalia Iyudu and Stanislav Shkarin

A three dimensional Sklyanin is the quadratic algebra over a field Equation with 3 generators x; y; z given by 3 relations xy - ayx - szz = 0, yz - azy - sxx = 0 and zx - axz - syy = 0, where a,s ∈ Equation . A generalized Sklyanin algebra is the algebra given by relations xy - a1yx - s1zz = 0, yz - a2zy - s2xx = 0 and zx - a3xz - s3yy = 0, where ai, siEquation . In this paper we announce the following results; the complete proofs will appear elsewhere. We determine explicitly the parameters for which these algebras has the same Hilbert series as the algebra of commutative polynomials in 3 indeterminates as well as when these algebras are Koszul and PBW, using constructive combinatorial methods. These provide new direct proofs of results established first by Artin, Tate, and Van Den Bergh.

исследовательская статья

Representations of Six-dimensional Mubarakazyanov Lie algebras

G Thompson, C Hettiarachchi, N Jones and A Shabanskaya4

A corrected list of the Mubarakzyanov algebras, that is, six-dimensional indecomposable solvable Lie algebras for which the nilradical is five-dimensional, is presented. For each class of algebra a matrix representation and a system of vector fields representation is given. As a consequence it follows that the dimension of the minimal matrix representation of any six-dimensional Lie algebra is at most six.

исследовательская статья

Examples of Freudenthal-Kantor Triple Systems

Norikai kamiya

Symmetry group of Lie algebras and superalgebras constructed from (ϵ,δ) Freudenthal-Kantor triple systems has been studied. Also, the definition and examples of hermitian triple systems is introduced in this note.

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