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## Banach Center Publications

1997 | 40 | 1 | 21-40
Tytuł artykułu

### Semilinear relations and *-representations of deformations of so(3)

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study a family of commuting selfadjoint operators $𝔸=(A_k)_{k=1}^n$, which satisfy, together with the operators of the family $𝔹=(B_j)_{j=1}^{n}$, semilinear relations $⅀ _{i} f_{ij}(𝔸) B_j g_{ij}(𝔸) = h(𝔸)$, ($f_{ij}$, $g_{ij}$, $h_j: ℝ^n → ℂ$ are fixed Borel functions). The developed technique is used to investigate representations of deformations of the universal enveloping algebra U(so(3)), in particular, of some real forms of the Fairlie algebra $U_q'(so(3))$.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
21-40
Opis fizyczny
Daty
wydano
1997
Twórcy
autor
• Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivska Str., Kiev, 252601 Ukraine
autor
• Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivska Str., Kiev, 252601 Ukraine
Bibliografia
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• [13] M. Havliček, A. U. Klimyk, E. Pelantová, Fairlie algebra $U_q'(so_3)$: oscillator realizations, root of unity, reduction $U_q(sl_3) ⊃ U_q'(so_3)$, J. Phys. A. (to appear)
• [14] S. A. Kruglyak and Yu. S. Samoĭlenko, On unitary equivalence of collections of self-adjoint operators, Funct. Anal. i Prilozhen. 14 (1980), no. 1, 60 - 62, (Russian).
• [15] V. L. Ostrovskiĭ and Yu. S. Samoĭlenko, Unbounded operators satisfying non-Lie commutation relations, Repts. Math. Phys. 28 (1989), no. 1, 91-103.
• [16] V. L. Ostrovskyĭ and Yu. S. Samoĭlenko, On pairs of self-adjoint operators, Seminar Sophus Lie 3 (1993), no. 2, 185-218.
• [17] V. L. Ostrovskyĭ and Yu. S. Samoĭlenko, Representations of *-algebras and dynamical system, Non-linear Math. Phys. 2 (1995), no. 2, 133-150.
• [18] V. L. Ostrovskyĭ and Yu. S. Samoĭlenko, On representations of the Heisenberg relations for the quantum e(2) group, Ukr. Mat. Zhurn. 47 (1995), no. 5, 700-710.
• [19] V. L. Ostrovskyĭ and L. B. Turovskaya, Representations of *-algebras and multidimensional dynamical systems, Ukr. Mat. Zhurn. 47 (1995), no. 4, 488-497.
• [20] A. Yu. Piryatinskaya and Yu. S. Samoĭlenko, Wild problems in representation theory of *-algebras with generators and relations, Ukr. Mat. Zhurn. 47 (1995), no. 1, 70-78.
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• [24] Yu. S. Samoĭlenko, Spectral theory of families of selfadjoint operators, 'Naukova Dumka', Kiev (1984) (Russian).
• [25] Yu. S. Samoĭlenko, V. S. Shul'man and L. B. Turovskaya, Semilinear relations and their *-representations, Preprint Augsburg, 1995.
• [26] Yu. S. Samoĭlenko and L. B. Turovskaya, On *-representations of semilinear relations, in: Met hods of Functional Analysis in problems of Mathematical Physics, Inst. Math Acad. Sci Ukraine, Kiev, (1992), 97-108.
• [27] Yu. S. Samoĭlenko and L. B. Turowska, Representations of cubic semilinear relations and real forms of the Fairlie algebra, Repts. Math. Phys. (to appear).
• [28] K. Schmüdgen, Unbounded operator algebras and representation theory, Akademie-Verlag, Berlin, (1990).
• [29] V. S. Shul'man, Multiplication operators and spectral synthesis, Dokl. Akad. Nauk SSSR 313 (1990), no. 5, (1047-1051); English transl. in Soviet Math. 42 (1991), no. 1.
• [30] Ya. S. Soibelman and L. L. Vaksman, The algebra of functions on the quantum group SU(n+1) and odd-dimensional quantum spheres, Algebra i Analiz. 2 (1990), no. 5, 101-120.
• [31] L. Turovskaya, Representations of some real forms of $U_q(sl(3))$, Algebras, groups and geometries, 12 (1995), 321-338.
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• [35] D. P. Zhelobenko, Compact Lie groups and their representations, 'Nauka', Moscow, (1970) (Russian).
Typ dokumentu
Bibliografia
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