Creutzig T (2024)
Publication Type: Journal article
Publication year: 2024
Book Volume: 110
Article Number: e70037
Journal Issue: 6
DOI: 10.1112/jlms.70037
The category of weight modules (Formula presented.) of the simple affine vertex algebra of (Formula presented.) at an admissible level (Formula presented.) is neither finite nor semisimple and modules are usually not lower-bounded and have infinite-dimensional conformal weight subspaces. However, this vertex algebra enjoys a duality with (Formula presented.), the simple principal (Formula presented.) -algebra of (Formula presented.) at level (Formula presented.) (the (Formula presented.) super conformal algebra) where the levels are related via (Formula presented.). Every weight module of (Formula presented.) is lower-bounded and has finite-dimensional conformal weight spaces. The main technical result is that every weight module of (Formula presented.) is (Formula presented.) -cofinite. The existence of a vertex tensor category follows and the theory of vertex superalgebra extensions implies the existence of vertex tensor category structure on (Formula presented.) for any admissible level (Formula presented.). As applications, the fusion rules of ordinary modules with any weight module are computed, and it is shown that (Formula presented.) is a ribbon category if and only if (Formula presented.) is, in particular, it follows that for admissible levels (Formula presented.) and (Formula presented.) and (Formula presented.), the category (Formula presented.) is a ribbon category.
APA:
Creutzig, T. (2024). Tensor categories of weight modules of sl̂2 at admissible level. Journal of the London Mathematical Society-Second Series, 110(6). https://doi.org/10.1112/jlms.70037
MLA:
Creutzig, Thomas. "Tensor categories of weight modules of sl̂2 at admissible level." Journal of the London Mathematical Society-Second Series 110.6 (2024).
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