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

• Date: 2013
• Main Authors: Proskurin, D. P., Yakymiv, R. Ya., Проскурін, Д. П., Якимів, Р. Я.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2013
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2437
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 =...