Geodesic
On $\ast$-representations of the $\mathbf Z_2$-graded extension of the quantum group $U_q(2)$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected problems of mathematical physics and analysis, Tome 203 (1994), pp. 202-214 
I. Ya. Aref'eva; G. E. Arutyunov. On $\ast$-representations of the $\mathbf Z_2$-graded extension of the quantum group $U_q(2)$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected problems of mathematical physics and analysis, Tome 203 (1994), pp. 202-214. http://geodesic.mathdoc.fr/item/TM_1994_203_a19/
@article{TM_1994_203_a19,
     author = {I. Ya. Aref'eva and G. E. Arutyunov},
     title = {On $\ast$-representations of the $\mathbf Z_2$-graded extension of the quantum group $U_q(2)$},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {202--214},
     year = {1994},
     volume = {203},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_1994_203_a19/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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 $U_q(2)$.