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Morita equivalences for Zhu's algebra
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abstract
Through the introduction of new ideals, and with the assistance of the $d$-th mode transition algebras $\mathfrak{A}_d$, for $d\in \mathbb{N}$, we show how Zhu's associative algebra $\mathsf{A}$, conventionally valued for tracking information about the degree $0$ part of an $\mathbb{N}$-graded module over a vertex operator algebra $V$, also contains information about components of higher degree. As an application, equivalent conditions are given for rationality of $V$, and explicit presentations for higher-level Zhu algebras are given, including for a large class of non-rational VOAs.
Forward citations
Cited by 3 Pith papers
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Modular functors from conformal blocks of rational vertex operator algebras
Spaces of conformal blocks of a strongly rational vertex operator algebra form a modular functor, giving the module category a modular fusion structure and a 3D topological field theory extension.
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Universal affine sl₂ vacuum VOAs are never strongly unital at k ≠ −2; for L_{ŝl₂}(1,0) an explicit strong-unit formula is given, but it fails for d ≥ 2 under the paper's own affine bracket conventions.
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How are pseudo-$q$-traces related to (co)ends?
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