Vasyl Ostrovskyi
@imath.kiev.ua
Institue of Mathematics, NAS of Ukraine
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Scopus Publications
V.L. Ostrovskyi, D.P. Proskurin, and R.Ya. Yakymiv
Vasyl Stefanyk Precarpathian National University
We consider families of power partial isometries satisfying twisted commutation relations with deformation parameters $\\lambda_{ij}\\in\\mathbb C$, $|\\lambda_{ij}|=1$. Irreducible representations of such a families are described up to the unitary equivalence. Namely any such representation corresponds, up to the unitary equivalence, to irreducible representation of certain higher-dimensional non-commutative torus.
Alexey Kuzmin, Vasyl Ostrovskyi, Danylo Proskurin, Moritz Weber, and Roman Yakymiv
World Scientific Pub Co Pte Ltd
We consider the [Formula: see text]-algebra [Formula: see text], which is a [Formula: see text]-twist of two Cuntz–Toeplitz algebras. For the case [Formula: see text], we give an explicit formula which untwists the [Formula: see text]-deformation showing that the isomorphism class of [Formula: see text] does not depend on [Formula: see text]. For the case [Formula: see text], we give an explicit description of all ideals in [Formula: see text]. In particular, we show that [Formula: see text] contains a unique largest ideal [Formula: see text]. We identify [Formula: see text] with the Rieffel deformation of [Formula: see text] and use a K-theoretical argument to show that the isomorphism class does not depend on [Formula: see text]. The latter result holds true in a more general setting of multiparameter deformations.
Vasyl Ostrovskyi and Danylo Yakymenko
Springer Science and Business Media LLC
Olha Ostrovska, Vasyl Ostrovskyi, Danylo Proskurin, and Yurii Samoilenko
National Pedagogical Dragomanov University
Vasyl Ostrovskyi and Konrad Schmüdgen
Springer Science and Business Media LLC
V. L. Ostrovskyi and Yu. S. Samoilenko
Springer Science and Business Media LLC
VASYL OSTROVSKYI, DANIIL PROSKURIN, YURII SAVCHUK, and LYUDMILA TUROWSKA
World Scientific Pub Co Pte Lt
We study a Wick ideal structure of quadratic *-algebras allowing Wick ordering with braided operator of coefficients. A construction of nested sequence of homogeneous Wick ideals of growing degree is presented. Representations of a Wick analogue of the CCR algebra with two degrees of freedom, annihilating certain homogeneous Wick ideals are described.
Vasyl Ostrovskyi, Daniil Proskurin, and Lyudmila Turowska
Springer Science and Business Media LLC
Vasyl Ostrovskyi, Stanislav Popovych, and Lyudmila Turowska
Elsevier BV
Sergio Albeverio, Vasyl Ostrovskyi, and Yurii Samoilenko
Elsevier BV
V. L. Ostrovs’kyi and Yu. S. Samoilenko
Springer Science and Business Media LLC
V. L. Ostrovs’kyi
Springer Science and Business Media LLC
A.A. Mohammad and M. Can
Springer Science and Business Media LLC
1. The theory of representations ofA (∗-homomorphisms π:A 7→ L(H) of a ∗-algebraA into a ∗-algebra L(H) of all bounded operators or into a ∗-algebra of unbounded operators in a separable complex Hilbert space H) is important both in mathematics and in physical applications. The ∗-representations of A (a local object) contain information about the structure of the algebra itself as well as about the structure of its dual object. Studying a particular class of representations of A in general by unbounded operators allows to define the corresponding non-commutative manifold: a C∗-algebra A (a global object) which possesses this class of representations. A choice of a particular representation π(·) corresponds to the choice of a model with observables Ak = π(ak) (k = 1, . . . , n) obeying the relations
V. L. Ostrovskii and L. B. Turovskaya
Springer Science and Business Media LLC
Vasyl' L. Ostrovs'kyĭ and Yurii S. Samoilenko
Springer Science and Business Media LLC
Here Pk(·) are polynomials in the non-commuting variables a1, . . . , an over C such that P ∗ k (·) = Pk(·). In other words, A is a quotient of the free ∗-algebra C〈a1, . . . , an〉 generated by the self-adjoint elements a1, . . . , an with respect to the two-sided ideal generated by the relations (1). Representations ot A (∗-homomorphisms π:A → L(H) of the ∗-algebra A into a ∗algebra L(H) of bounded operators on a separable Hilbert space H or into a ∗-algebra of unbounded operators) are of interest both from mathematical point of view and for their physical applications. A choice of a representation π(·) corresponds to a choice of a model with observables Ak = π(ak) (k = 1, . . . , n), which are connected by the relations Pk(A1, . . . , An) = 0 (k = 1, . . . ,m). (2)
V. L. Ostrovs'kyi and Yu. S. Samoilenko
Springer Science and Business Media LLC
Vasyl L. Ostrovskyĭ and YuriĭS. Samoĭlenko
Elsevier BV
V. L. Ostrovskii and Yu. S. Samoilenko
Springer Science and Business Media LLC
V. L. Ostrovskii and S. D. Sil'vestrov
Springer Science and Business Media LLC
V. L. Ostrovskii and Yu. S. Samoilenko
Springer Science and Business Media LLC
V. L. Ostrovskii and Yu. S. Samoilenko
Springer Science and Business Media LLC
V.L. Ostrovskii and Yu.S. Samoilenko
Elsevier BV
V. L. Ostrovskii and Yu. S. Samoilenko
Springer Science and Business Media LLC
Yu. M. Berezanskii, V. L. Ostrovskii, and Yu. S. Samoilenko
Springer Science and Business Media LLC