arXiv subjects
Publications and source records attributed to Mizuki Oikawa.
We define the notion of the $(G,Γ)$-crossed center of a $(G,Γ)$-crossed tensor category in the sense of Natale. We show that the $(G, Γ)$-crossed center is a $(G \bowtie Γ, G \times Γ)$-braided tensor category. This construction generalizes the graded center construction for graded tensor categories and the equivariant center construction for tensor categories with group actions.
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.