On families of twisted power partial isometries 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.
On q-tensor products of Cuntz algebras 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.
On the structure of homogenenous wick ideals in wick <inf>*</inf>- algebras with braided coefficients 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.
Representation Theory and Numerical AF-Invariants: The Representations and Centralizers of Certain States on script O sing d
On representations of *-algebras in mathematical physics 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
Representations of *-algebras and dynamical systems 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)
On families of twisted power partial isometries VL Ostrovskyi, DP Proskurin, RY Yakymiv Carpathian Mathematical Publications 14 (1), 260-265 2022
On -tensor products of Cuntz algebras A Kuzmin, V Ostrovskyi, D Proskurin, M Weber, R Yakymiv International Journal of Mathematics 33 (02), 2250017 2022
Geometric properties of SIC-POVM tensor square V Ostrovskyi, D Yakymenko Letters in Mathematical Physics 112 (1), 7 2022
A class of representations of -algebra generated by -commuting isometries O Ostrovska, V Ostrovskyi, D Proskurin, Y Samoilenko arXiv preprint arXiv:2111.13059 2021
On representations of q_ij-commuting isometries V Ostrovskyi, O Ostrovska, D Proskurin, Y Samoilenko 2021
Про зображення алгебр, породжених скінченним розкладом одиниці та набором ортогональних проекторів EN Ashurova, VL Ostrovskyi, YS Samoilenko Reports of the National Academy of Sciences of Ukraine, 3-9 2017
On representations of “all but two” algebras EN Ashurova, VL Ostrovskyi Zbirnyk Prats Instytutu Matematyky NAN Ukrainy 12, 8-21 2015
A resolvent approach to the real quantum plane V Ostrovskyi, K Schmdgen Integral Equations and Operator Theory 79, 451-476 2014
Some remarks on Hilbert representations of posets V Ostrovskyi, S Rabanovich arXiv preprint arXiv:1312.2920 2013
О парах операторов, связанных квадратичным соотношением ВЛ Островский, ЮС Самойленко Функциональный анализ и его приложения 47 (1), 82-87 2013
Зображення канонічних антикомутаційних співвідношень з умовою ортогональності ВЛ Островський, ОВ Островська, ДП Проскурін, РЯ Якимів 2013
Representations of relations with orthogonality condition and their deformations VL Ostrovskyi, DP Proskurin, RY Yakymiv Methods of Functional Analysis and Topology 18 (04), 373-386 2012
On the Structure of Homogenenous Wick Ideals in Wick*-ALGEBRAS with Braided Coefficients V Ostrovskyi, D Proskurin, Y Savchuk, L Turowska Reviews in Mathematical Physics 24 (04), 1250007 2012
Конечномерный линейный анализ. I. Линейные операторы в конечномерных векторных пространствах (L) МА Муратов, ВЛ Островский, ЮС Самойленко Киев: Центр учеб. лит 2011
Unbounded Representations of q-Deformation of Cuntz Algebra V Ostrovskyi, D Proskurin, L Turowska Letters in Mathematical Physics 85 (2), 147-162 2008
On C∗-algebra of a semigroup of partial isometries V Ostrovskyi, S Popovych, L Turowska Journal of Functional Analysis 251 (1), 210-231 2007
On quadruples of linearly connected projections and transitive systems of subspaces Y Moskaleva, V Ostrovskyi, K Yusenko Methods of Functional Analysis and Topology 13 (01), 43-49 2007
On functions on graphs and representations of a certain class of∗-algebras S Albeverio, V Ostrovskyi, Y Samoilenko Journal of Algebra 308 (2), 567-582 2007
On spectral theorems for families of linearly connected self-adjoint operators with given spectra associated with extended Dynkin graphs VL Ostrovs’ kyi, YS Samoilenko Ukrainian Mathematical Journal 58 (11), 1768-1785 2006
Special characters on star graphs and representations of -algebras V Ostrovskyi arXiv preprint math/0509240 2005
MOST CITED SCHOLAR PUBLICATIONS
Introduction To The Theory Of Representations of Finitely Presented *-Algebras. I. Representations by Bounded Operators V Ostrovskyi, Y Samoilenko CRC Press 2004 Citations: 192
Representation theory and numerical AF-invariants: The representations and centralizers of certain states on Od O Bratteli, PET Jrgensen, V Ostrovsʹkyĭ American Mathematical Soc. 168 (797) 2004 Citations: 44
On functions on graphs and representations of a certain class of∗-algebras S Albeverio, V Ostrovskyi, Y Samoilenko Journal of Algebra 308 (2), 567-582 2007 Citations: 39
On spectral theorems for families of linearly connected self-adjoint operators with given spectra associated with extended Dynkin graphs VL Ostrovs’ kyi, YS Samoilenko Ukrainian Mathematical Journal 58 (11), 1768-1785 2006 Citations: 21
On pairs of self-adjoint operators VL Ostrovskyı, YS Samoılenko Seminar Sophus Lie 3 (2), 185-218 1993 Citations: 18
Expansion in eigenfunctions of families of commuting operators and representations of commutation relations YM Berezanskii, VL Ostrovskii, YS Samoilenko Ukrainian Mathematical Journal 40, 90-92 1988 Citations: 15
Representations of real-valued forms of the graded analogue of a Lie algebra VL Ostrovskii, SD Sil'vestrov Ukrainian Mathematical Journal 44 (11), 1395-1401 1993 Citations: 14
On*-representations of a certain class of algebras related to a graph V Ostrovskyi arXiv preprint math/0506505 2005 Citations: 13
Representations of -algebras with two generators and polynomial relations VL Ostrovskii, YS Samoilenko Zapiski Nauchnykh Seminarov POMI 172, 121-129 1989 Citations: 13
On -tensor products of Cuntz algebras A Kuzmin, V Ostrovskyi, D Proskurin, M Weber, R Yakymiv International Journal of Mathematics 33 (02), 2250017 2022 Citations: 12
Families of unbounded self-adjoint operators connected by non-Lie relations VL Ostrovskii, YS Samoilenko Functional Analysis and Its Applications 23 (2), 139-141 1989 Citations: 12
Representations of∗-algebras and multidimensional dynamical systems VL Ostrovskyı, LB Turovskaya Ukr. Mat. Zhurn 47 (4), 488-497 1995 Citations: 11
Structure theorems for a pair of unbounded selfadjoint operators satisfying quadratic relation VL Ostrovskii, YS Samoilenko Akad. Nauk Ukrain. SSR. Inst. Mat. Preprint, 1-25 1991 Citations: 11
Representations of quadratic∗-algebras by bounded and unbounded operators VL Ostrovskyĭ, YS Samoĭlenko Reports on Mathematical Physics 35 (2-3), 283-301 1995 Citations: 9
Representations of the real forms of a graded analogue of the Lie algebra sl (2, C) VL Ostrovskyi, SD Silvestrov Ukr. Mat. Zhurn 44 (11), 1518-1524 1992 Citations: 9
Unbounded Representations of q-Deformation of Cuntz Algebra V Ostrovskyi, D Proskurin, L Turowska Letters in Mathematical Physics 85 (2), 147-162 2008 Citations: 8
Special characters on star graphs and representations of -algebras V Ostrovskyi arXiv preprint math/0509240 2005 Citations: 8