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Trudy Matematicheskogo Instituta im. V. A. Steklova, 1994, Volume 203, Pages 202–214 (Mi tm1305)  

This article is cited in 1 scientific paper (total in 1 paper)

On $\ast$-representations of the $\mathbf Z_2$-graded extension of the quantum group $U_q(2)$

I. Ya. Aref'eva, G. E. Arutyunov

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (934 kB) Citations (1)
Abstract: The possibility of introducing an involution for the $Z_2$-graded extension of the function algebra on the quantum group $GL_q(N)$ is discussed. The involution permits the quantum group $GL_q(N)$ to have the compact form which is $U_q(N)$. However, the compact form related to $SU_q(N)$ is not allowed. $\ast$-representations of the $Z_2$-graded extension of $U_q(2)$ in a Hilbert space are constructed. The operators corresponding to the differentials are expressed as derivations on the space of all irreducible $\ast$-representations of $U_q(2)$.
Received in May 1993
Bibliographic databases:
Document Type: Article
UDC: 512.5
Language: English
Citation: I. Ya. Aref'eva, G. E. Arutyunov, “On $\ast$-representations of the $\mathbf Z_2$-graded extension of the quantum group $U_q(2)$”, Selected problems of mathematical physics and analysis, Collection of articles. To seventy birthday of Academician V. S. Vladimirov, Trudy Mat. Inst. Steklov., 203, Nauka, Moscow, 1994, 202–214; Proc. Steklov Inst. Math., 203 (1995), 181–189
Citation in format AMSBIB
\Bibitem{AreAru94}
\by I.~Ya.~Aref'eva, G.~E.~Arutyunov
\paper On $\ast$-representations of the $\mathbf Z_2$-graded extension of the quantum group $U_q(2)$
\inbook Selected problems of mathematical physics and analysis
\bookinfo Collection of articles. To seventy birthday of Academician V. S. Vladimirov
\serial Trudy Mat. Inst. Steklov.
\yr 1994
\vol 203
\pages 202--214
\publ Nauka
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm1305}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1382605}
\zmath{https://zbmath.org/?q=an:0897.17016}
\transl
\jour Proc. Steklov Inst. Math.
\yr 1995
\vol 203
\pages 181--189
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  • This publication is cited in the following 1 articles:
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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