2017
Том 69
№ 9

All Issues

On *-representations of λ-deformations of canonical commutation relations

Proskurin D. P., Yakymiv R. Ya.

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Abstract

We study irreducible integrable *-representations of the algebra $\mathfrak{U}_{\lambda, 2}$ generated by the following relations: $$\mathfrak{U}_{\lambda, 2} = \mathbb{C} \langle a_j, a_j^{*} \,| \,a_j^{*} a_j = 1 + a_ja_j^{*},\; a_1^{*}a_2 = \lambda a_2a_1^{*},\; a_2a_1 = \lambda a_1 a_2,\; j = 1, 2 \rangle .$$ For this *-algebra, we prove an analog of the von Neumann theorem on the uniqueness of an irreducible integrable representation.

English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 4, pp 593-601.

Citation Example: Proskurin D. P., Yakymiv R. Ya. On *-representations of λ-deformations of canonical commutation relations // Ukr. Mat. Zh. - 2013. - 65, № 4. - pp. 538-545.

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