Rigid Tensor Structure on Big Module Categories for Some W-(super)algebras in Type A

Creutzig, Thomas; McRae, Robert; Yang, Jinwei

doi:10.1007/s00220-023-04843-1

Commun. Math. Phys.

2023

DOI: 10.1007/s00220-023-04843-1

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Rigid Tensor Structure on Big Module Categories for Some W-(super)algebras in Type A

Thomas Creutzig,

Robert McRae,

Jinwei Yang

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2024

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Cited by 3 publications

References 89 publications

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Quasi-lisse extension of affine sl2 à la Feigin–Tipunin

Creutzig,

Nakatsuka,

Sugimoto

2024

Advances in Mathematics

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Quasi-lisse extension of affine sl2 à la Feigin–Tipunin

Creutzig,

Nakatsuka,

Sugimoto

2024

Advances in Mathematics

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Tensor category KLk(sl2n) via minimal affine W-algebras at the non-admissible level
Adamović,
Creutzig,
Perše
et al. 2024
Journal of Pure and Applied Algebra
1
0
0
0
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Tensor categories of weight modules of sl̂2$\widehat{\mathfrak {sl}}_2$ at admissible level

Creutzig

2024

Journal of London Math Soc

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The category of weight modules of the simple affine vertex algebra of at an admissible level 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 , the simple principal ‐algebra of at level (the super conformal algebra) where the levels are related via . Every weight module of is lower‐bounded and has finite‐dimensional conformal weight spaces. The main technical result is that every weight module of is ‐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 for any admissible level . As applications, the fusion rules of ordinary modules with any weight module are computed, and it is shown that is a ribbon category if and only if is, in particular, it follows that for admissible levels and and , the category is a ribbon category.

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Rigid Tensor Structure on Big Module Categories for Some W-(super)algebras in Type A

Cited by 3 publications

References 89 publications

Quasi-lisse extension of affine sl2 à la Feigin–Tipunin

Quasi-lisse extension of affine sl2 à la Feigin–Tipunin

Tensor category KLk(sl2n) via minimal affine W-algebras at the non-admissible level
Adamović,
Creutzig,
Perše
et al. 2024
Journal of Pure and Applied Algebra
1
0
0
0
View full text Add to dashboard Cite

Tensor categories of weight modules of sl̂2$\widehat{\mathfrak {sl}}_2$ at admissible level

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Rigid Tensor Structure on Big Module Categories for Some W-(super)algebras in Type A

Cited by 3 publications

References 89 publications

Quasi-lisse extension of affine sl2 à la Feigin–Tipunin

Quasi-lisse extension of affine sl2 à la Feigin–Tipunin

Tensor category KLk(sl2n) via minimal affine W-algebras at the non-admissible level Adamović, Creutzig, Perše et al. 2024Journal of Pure and Applied Algebra1000View full textAdd to dashboardCite

Tensor categories of weight modules of sl̂2$\widehat{\mathfrak {sl}}_2$ at admissible level

Contact Info

Product

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About

Tensor category KLk(sl2n) via minimal affine W-algebras at the non-admissible level
Adamović,
Creutzig,
Perše
et al. 2024
Journal of Pure and Applied Algebra
1
0
0
0
View full text Add to dashboard Cite