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- W3136359307 abstract "Let $Vsubseteq A$ be a conformal inclusion of vertex operator algebras and let $mathcal{C}$ be a category of grading-restricted generalized $V$-modules that admits the vertex algebraic braided tensor category structure of Huang-Lepowsky-Zhang. We give conditions under which $mathcal{C}$ inherits semisimplicity from the category of grading-restricted generalized $A$-modules in $mathcal{C}$, and vice versa. The most important condition is that $A$ be a rigid $V$-module in $mathcal{C}$ with non-zero categorical dimension, that is, we assume the index of $V$ as a subalgebra of $A$ is finite and non-zero. As a consequence, we show that if $A$ is strongly rational, then $V$ is also strongly rational under the following conditions: $A$ contains $V$ as a $V$-module direct summand, $V$ is $C_2$-cofinite with a rigid tensor category of modules, and $A$ has non-zero categorical dimension as a $V$-module. These results are vertex operator algebra interpretations of theorems proved for general commutative algebras in braided tensor categories. We also generalize these results to the case that $A$ is a vertex operator superalgebra." @default.
- W3136359307 created "2021-03-29" @default.
- W3136359307 creator A5030450639 @default.
- W3136359307 date "2022-03-14" @default.
- W3136359307 modified "2023-10-16" @default.
- W3136359307 title "On semisimplicity of module categories for finite non-zero index vertex operator subalgebras" @default.
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- W3136359307 doi "https://doi.org/10.1007/s11005-022-01523-4" @default.
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