hyperoctahedral_series
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| - | The quantum groups of the hyperoctahedral series are [[group-theoretical hyperoctahedral orthogonal easy quantum groups]] and can therefore be written as semi-direct products with their diagonal subgroups [(:ref:RaWe15)]: $$C(H_N^{(s)})\cong C^\ast\langle \{a_i\}_{i=1}^n \,\vert\, \forall_{i,j=1}^n: a_i^2=1,\, (a_ia_j)^s=1,\,\forall_{i,j,k=1}^n: a_i a_k a_j=a_j a_k a_i \rangle\bowtie C(S_N)$$ | + | The quantum groups of the hyperoctahedral series are [[group-theoretical_hyperoctahedral_easy_orthogonal_quantum_groups|group-theoretical hyperoctahedral orthogonal easy quantum groups]] and can therefore be written as semi-direct products with their diagonal subgroups [(:ref:RaWe15)]: $$C(H_N^{(s)})\cong C^\ast\langle \{a_i\}_{i=1}^n \,\vert\, \forall_{i,j=1}^n: a_i^2=1,\, (a_ia_j)^s=1,\,\forall_{i,j,k=1}^n: a_i a_k a_j=a_j a_k a_i \rangle\bowtie C(S_N)$$ |
| for all $s,N\in \N$ with $s\geq 3$, where $C(S_N)$ denotes the continuous function over the symmetric group of dimension $N$ (considered as the subgroup of $\mathrm{GL}(\C,N)$ given by all [[wp>permutation matrices]]). | for all $s,N\in \N$ with $s\geq 3$, where $C(S_N)$ denotes the continuous function over the symmetric group of dimension $N$ (considered as the subgroup of $\mathrm{GL}(\C,N)$ given by all [[wp>permutation matrices]]). | ||
hyperoctahedral_series.1580110931.txt.gz · Last modified: 2021/11/23 11:56 (external edit)
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