arXiv subjects

Chunrui Ai

Publications and source records attributed to Chunrui Ai.

6 recordsLinked to original sources

arXiv2024

Semisimplicity of module categories of certain affine vertex operator superalgebras

In this paper, we show Kazhdan-Lusztig categories, that is, the categories of lower bounded generalized weight modules for certain affine vertex operator superalgebras that are locally finite modules of the underlying finite dimensional Lie superalgebra, are semisimple. Those are all representation categories of affine vertex operator superalgebras at conformal but non admissible levels. As a consequence, the categories of finite length generalized modules for these affine vertex operator superalgebras have braided tensor category structures.

math.QA↗

arXiv2021

Module category and $C_2$-cofiniteness of affine vertex operator superalgebras

In this paper, we investigate the Lie algebra structures of weight one subspaces of $C_2$-cofinite vertex operator superalgebras. We also show that for any positive integer $k$, vertex operator superalgebras $L_{sl(1|n+1)}(k,0)$ and $L_{osp(2|2n)}(k,0)$ have infinitely many irreducible admissible modules. As a consequence, we give a proof of the fact that $L_{\mathfrak g}(k,0)$ is $C_2$-cofinite if and only if $\mathfrak g$ is either a simple Lie algebra, or $\mathfrak g=osp(1|2n)$, and $k$ is a nonnegative integer. As an application, we show that $L_{G(3)}(1,0)$ is a vertex operator superalgebra such that the category of $L_{G(3)}(1,0)$-modules is semisimple but $L_{G(3)}(1,0)$ is not $C_2$-cofinite.

math.QA↗

arXiv2018

Some exceptional extensions of Virasoro vertex operator algebras

In this paper, extensions of nonunitary rational Virasoro vertex operator algebras corresponding to some exceptional modular invariants are constructed. The uniqueness of these extensions is also established.

math.QA↗

arXiv2016

The classification of extensions of $L_{sl_3}(k,0)$

IIn this paper, extensions of affine vertex operator algebras $L_{sl_3}(k,0)$, $k\in \mathbb{Z}_+$, are classified by modular invariants.

math.QA↗

arXiv2016

The irreducible modules and fusion rules for the parafermion vertex operator algebras

The irreducible modules for the parafermion vertex operator algebra associated to any finite dimensional Lie algebra and any positive integer are identified, the quantum dimensions are computed and the fusion rules are determined.

math.QA↗

arXiv2015

On the unitary structures of vertex operator superalgebras

In this paper, the notion of unitary vertex operator superalgebra is introduced. It is proved that the vertex operator superalgebras associated to the unitary highest weight representations for the Neveu-Schwarz Lie superalgebra, Heisenberg superalgebras and to positive definite integral lattices are unitary vertex operator superalgebras. The unitary structures are then used to study the structures of vertex operator superalgebras, it is proved that any unitary vertex operator superalgebra is a direct sum of strong CFT type unitary simple vertex operator superalgebras. The classification of unitary vertex operator superalgebras generated by the subspaces with conformal weights less than or equal to $1$ is also considered.

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