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- W3154642787 abstract "Let $V$ be a vertex operator superalgebra with the natural order 2 automorphism $sigma$. Under suitable conditions on $V$, the $sigma$-fixed subspace $V_{bar 0}$ is a vertex operator algebra and the category $C_{V_{bar 0}}$ of $V_{bar 0}$-modules is modular tensor category. In this paper, we prove that $C_{V_{bar 0}}$ is a fermionic modular tensor category and the Muger centralizer $C_{V_{bar 0}}^0$ of the fermion in $C_{V_{bar 0}}$ is generated by the irreducible $V_{bar 0}$-submodules of the $V$-modules. In particular, $C_{V_{bar 0}}^0$ is a super-modular tensor category and $C_{V_{bar 0}}$ is a minimal modular extension of $C_{V_{bar 0}}^0$. We provide a construction of a vertex operator $V^l$ for each positive integer $l$ such that $C_{V^l_{bar 0}}$ is minimal modular extension of $C_{V_{bar 0}}^0$. We prove that these modular tensor categories $C_{V^l_{bar 0}}$ are uniquely determined, up to equivalence, by the congruence class of $l$ modulo 16." @default.
- W3154642787 created "2021-04-26" @default.
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- W3154642787 date "2021-04-16" @default.
- W3154642787 modified "2023-10-16" @default.
- W3154642787 title "Vertex operator superalgebras and 16-fold way" @default.
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- W3154642787 doi "https://doi.org/10.1090/tran/8454" @default.
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