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## Banach Center Publications

1997 | 40 | 1 | 59-65
Tytuł artykułu

### On *-representations of $U_{q}(sl(2))$: more real forms

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EN
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EN
The main goal of this paper is to do the representation-theoretic groundwork for two new candidates for locally compact (nondiscrete) quantum groups. These objects are real forms of the quantized universal enveloping algebra $U_q(sl(2))$ and do not have real Lie algebras as classical limits. Surprisingly, their representations are naturally described using only bounded (in one case only two-dimensional) operators. That removes the problem of describing their Hopf structure 'on the Hilbert space level'([W]).
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Tom
Numer
Strony
59-65
Opis fizyczny
Daty
wydano
1997
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autor
• Department of Mathematics, UCLA, 405 Hilgard Ave., Los Angeles, California 90095-1555, USA
Bibliografia
• [CP] A. Pressley, V. Chari, A guide to quantum groups, Cambridge Univ. Press, Cambridge, 1994.
• [J] M. Jimbo, A q-difference analog of U(𝐺) and the Yang-Baxter equation, Lett. Math. Phys. 10 (1985), 63-69.
• [L] G. Lusztig, Modular representations and quantum groups, Contemp. Math. 82. Classical groups and related topics, Amer. Math. Soc., Providence, 1990, pp. 59-77.
• [MM] T. Masuda, K. Mimachi, Y. Nakagami, M. Noumi, Y. Saburi, K. Ueno, Unitary representations of the quantum group $SU_q (1,1)$, Lett. Math. Phys. 19 (1990), 187-204.
• [T] E. Twietmeyer, Real forms of $U_q(𝐺)$, Lett. Math. Phys. 24 (1992), 49-58.
• [V1] E. Vaysleb, Infinite-dimensional *-representations of the Sklyanin algebra and of the quantum algebra $U_q(sl(2))$, Selecta Mathematica formerly Sovietica 12 (1993), 57-73.
• [V2] E. Vaysleb, Collections of commuting selfadjoint operators satisfying some relations with a non-selfadjoint one, Ukrain. Matem. Zh. 42 (1990), 1258-1262; Engish transl. in Ukrain. Math. J. 42 (1990), 1119-1123.
• [W] S. L. Woronowicz, Unbounded elements affiliated with C*-algebras and non-compact quantum groups, Commun. Math. Phys. 136 (1991), 399-432.
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