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
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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 $U_q(2)$.
@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},
publisher = {mathdoc},
volume = {203},
year = {1994},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TM_1994_203_a19/}
}
TY - JOUR AU - I. Ya. Aref'eva AU - G. E. Arutyunov TI - On $\ast$-representations of the $\mathbf Z_2$-graded extension of the quantum group $U_q(2)$ JO - Trudy Matematicheskogo Instituta imeni V.A. Steklova PY - 1994 SP - 202 EP - 214 VL - 203 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TM_1994_203_a19/ LA - en ID - TM_1994_203_a19 ER -
%0 Journal Article %A I. Ya. Aref'eva %A G. E. Arutyunov %T On $\ast$-representations of the $\mathbf Z_2$-graded extension of the quantum group $U_q(2)$ %J Trudy Matematicheskogo Instituta imeni V.A. Steklova %D 1994 %P 202-214 %V 203 %I mathdoc %U http://geodesic.mathdoc.fr/item/TM_1994_203_a19/ %G en %F TM_1994_203_a19
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/