The Zhu algebra variety conjecture for finitely strongly generated simple vertex operator algebras

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Let VV be a finitely strongly generated simple vertex operator algebra of CFT type. Write

Var⁡A(V):=Specm⁡gr⁡F(A(V)).\operatorname{Var} A(V):=\operatorname{Specm}\operatorname{gr}_F(A(V)).

Here XVX_V denotes the associated variety of VV. The Zhu algebra variety conjecture. We have an isomorphism of affine varieties

Var⁡A(V)≅XV.\operatorname{Var} A(V)\cong X_V.

This statement is presented as a conjecture in the source and concerns the relationship between the associated variety of a vertex operator algebra and the maximal spectrum of the associated graded Zhu algebra; the supplied text gives no evidence of a resolution.

References

Primary source

Tomoyuki Arakawa, “Rationality of W-algebras: principal nilpotent cases”, arXiv:1211.7124 (2015).

Additional references

2 papers in this index state this conjecture (2007–2012). The statement above is taken from the most recent of them; the others are arXiv:0712.0379.

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