Frobenius algebras associated with the $α$-induction for equivariantly braided tensor categories
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929625626574848 |
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| author | Oikawa, Mizuki |
| author_facet | Oikawa, Mizuki |
| contents | Let $G$ be a group. We give a categorical definition of the $G$-equivariant $α$-induction associated with a given $G$-equivariant Frobenius algebra in a $G$-braided multitensor category, which generalizes the $α$-induction for $G$-twisted representations of conformal nets. For a given $G$-equivariant Frobenius algebra in a spherical $G$-braided fusion category, we construct a $G$-equivariant Frobenius algebra, which we call a $G$-equivariant $α$-induction Frobenius algebra, in a suitably defined category called neutral double. This construction generalizes Rehren's construction of $α$-induction Q-systems. Finally, we define the notion of the $G$-equivariant full center of a $G$-equivariant Frobenius algebra in a spherical $G$-braided fusion category and show that it indeed coincides with the corresponding $G$-equivariant $α$-induction Frobenius algebra, which generalizes a theorem of Bischoff, Kawahigashi and Longo. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11845 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Frobenius algebras associated with the $α$-induction for equivariantly braided tensor categories Oikawa, Mizuki Quantum Algebra Mathematical Physics Category Theory Operator Algebras Let $G$ be a group. We give a categorical definition of the $G$-equivariant $α$-induction associated with a given $G$-equivariant Frobenius algebra in a $G$-braided multitensor category, which generalizes the $α$-induction for $G$-twisted representations of conformal nets. For a given $G$-equivariant Frobenius algebra in a spherical $G$-braided fusion category, we construct a $G$-equivariant Frobenius algebra, which we call a $G$-equivariant $α$-induction Frobenius algebra, in a suitably defined category called neutral double. This construction generalizes Rehren's construction of $α$-induction Q-systems. Finally, we define the notion of the $G$-equivariant full center of a $G$-equivariant Frobenius algebra in a spherical $G$-braided fusion category and show that it indeed coincides with the corresponding $G$-equivariant $α$-induction Frobenius algebra, which generalizes a theorem of Bischoff, Kawahigashi and Longo. |
| title | Frobenius algebras associated with the $α$-induction for equivariantly braided tensor categories |
| topic | Quantum Algebra Mathematical Physics Category Theory Operator Algebras |
| url | https://arxiv.org/abs/2303.11845 |