For any finite group G there exists a McDuff II1 factor M such that its categorical Connes tilde-chi(M) is braided equivalent to Rep(G), providing the first non-modular braided fusion category realized this way.
On fusion categories.Ann
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Any unitary fusion category can be realized as symmetries on tensor products of infinite-dimensional Hilbert spaces via stabilized anyon chains, with equivalence between different chains of the same category.
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Gauging the Categorical Connes' $\tilde{\chi}(M)$
For any finite group G there exists a McDuff II1 factor M such that its categorical Connes tilde-chi(M) is braided equivalent to Rep(G), providing the first non-modular braided fusion category realized this way.
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Universal fusion category symmetries on tensor products of infinite-dimensional Hilbert spaces
Any unitary fusion category can be realized as symmetries on tensor products of infinite-dimensional Hilbert spaces via stabilized anyon chains, with equivalence between different chains of the same category.