free_orthogonal_quantum_group
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free_orthogonal_quantum_group [2019/02/28 11:57] d.gromada |
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| Free orthogonal quantum groups $O_N^+$ were first defined in [(:ref:Wang95)]. It is a one-parameter series of quantum groups forming a free counterpart to the orthogonal groups $O_N$ | Free orthogonal quantum groups $O_N^+$ were first defined in [(:ref:Wang95)]. It is a one-parameter series of quantum groups forming a free counterpart to the orthogonal groups $O_N$ | ||
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| ===== Definition ===== | ===== Definition ===== | ||
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| Free orthogonal quantum group of size $N$ is a compact matrix quantum group $O_N^+=(C(O_N^+),u)$, where | Free orthogonal quantum group of size $N$ is a compact matrix quantum group $O_N^+=(C(O_N^+),u)$, where | ||
| $$C(O_N^+)=C^*(u_{ij},\;i,j=1,\dots,n\mid u_{ij}=u_{ij}^*,\;uu^t=u^tu=1_{\mathbb{C}^N}).$$ | $$C(O_N^+)=C^*(u_{ij},\;i,j=1,\dots,n\mid u_{ij}=u_{ij}^*,\;uu^t=u^tu=1_{\mathbb{C}^N}).$$ | ||
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| ===== Representation theory ===== | ===== Representation theory ===== | ||
free_orthogonal_quantum_group.1551355070.txt.gz · Last modified: 2021/11/23 11:56 (external edit)
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