2019
Том 71
№ 11

# Proskurin D. P.

Articles: 3
Article (Ukrainian)

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

Ukr. Mat. Zh. - 2013. - 65, № 4. - pp. 538-545

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.

Article (Ukrainian)

### On ∗-representations of deformations of canonical anticommutation relations

Ukr. Mat. Zh. - 2010. - 62, № 2. - pp. 203–214

We consider irreducible ∗-representations of deformations of canonical anticommutation relations (CAR) that belong to the class of ∗-algebras generated by generalized quons.

Article (Russian)

### On C*-Algebras Generated by Deformations of CCR

Ukr. Mat. Zh. - 2004. - 56, № 11. - pp. 1527-1538

We consider C*-algebras generated by deformations of classical commutation relations (CCR), which are generalizations of commutation relations for generalized quons and twisted CCR. We show that the Fock representation is a universal bounded representation. We discuss the connection between the presented deformations and extensions of many-dimensional noncommutative tori.