arXiv subjects

Xiangyu Jiao

Publications and source records attributed to Xiangyu Jiao.

10 recordsLinked to original sources

arXiv2026

Twisted modules of $\frac{1}{2}\mathbb{Z}$-graded modular vertex superalgebras

In this paper, we investigate the theory of $g$-twisted modules for modular $\frac{1}{2}\mathbb{Z}$-graded vertex superalgebras over an algebraically closed field $\mathbb{F}$ of prime characteristic $p>2$. For a $\frac{1}{2}\mathbb{Z}$-graded vertex superalgebra $V$ and an automorphism $g$ of $V$ of finite order $T$ relatively prime to $p$, we give a twisted version of Zhu's associative algebra, denoted by $A_g(V)$. We prove that there is a one-to-one correspondence between the set of equivalence classes of simple $A_g(V)$-modules and the set of equivalence classes of simple $\frac{1}{T_0}\mathbb{N}$-graded $g$-twisted $V$-modules, where $T_0$ is the order of the automorphism $gσ$ with $σ$ the parity automorphism. As an application, we study twisted modules for modular vertex superalgebras associated to the affine Lie superalgebras and determine the corresponding twisted Zhu algebra. We also compute the twisted Zhu algebra for the modular Neveu-Schwarz vertex superalgebra and classify its irreducible twisted modules.

math.QA↗

arXiv2026

A unitary vertex operator algebra arising from the 3C-algebra

We give an algebraic proof of the unitarity of the vertex operator algebra $L(21/22, 0)\oplus L(21/22, 8)$ and of all its irreducible ordinary modules, using a coset realization arising from the $3C$-algebra. Motivated by the structure of the resulting module decomposition, we establish a general result on fusion rules for commutant vertex operator subalgebras within the framework of modular tensor categories. As an application of this general result, we explicitly determine the fusion rules of all irreducible $L(21/22, 0)\oplus L(21/22, 8)$-modules.

math.QA↗

arXiv2022

Vertex operator algebras generated by two Ising vectors

In this paper we mainly study the vertex operator algebra $\mathbb{C} \mathrm{VA}(e, f)$ generated by two Ising vectors $e$ and $f$ with $\langle e, f\rangle=\frac{5}{2^{10}}$. We prove $\mathbb{C} \mathrm{VA}(e, f)$ is isomorphic to the $6A$-algebra $\mathcal{U}_{6A}$ constructed by Lam-Yamada-Yamauchi. We also discuss the cases $\langle e, f\rangle=\frac{1}{4}, \frac{1}{2^{5}}, 0 $ and the case $\langle e, f\rangle=\frac{1}{2^{8}}$ with $(τ_{e}τ_{f})^4=1$.

math.QA↗

arXiv2019

$6A$-Algebra and its representations

In this paper, we study the structure and representation of a $6A$-algebra which is a vertex operator algebra generated by two Ising vectors $e,f$ with inner product $\left\langle e,f\right\rangle =\frac{5}{2^{10}}.$ In particular, we prove the uniqueness of the vertex operator algebra structure of this 6A-algebra, classify the irreducible modules, and determine the fusion rules.

math.QA↗

arXiv2017

Modular Virasoro Vertex Algebras and Affine Vertex Algebras

In this paper, we study Virasoro vertex algebras and affine vertex algebras over a general field of characteristic $p>2$. More specifically, we study certain quotients of the universal Virasoro and affine vertex algebras by ideals related to the $p$-centers of the Virasoro algebra and affine Lie algebras. Among the main results, we classify their irreducible $\mathbb{N}$-graded modules by explicitly determining their Zhu algebras and show that these vertex algebras have only finitely many irreducible $\mathbb{N}$-graded modules and they are $C_2$-cofinite.

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

Bimodule and twisted representation of vertex operator algebras

In this paper, for a vertex operator algebra $V$ with an automorphism $g$ of order $T,$ an admissible $V$-module $M$ and a fixed nonnegative rational number $n\in\frac{1}{T}\Bbb{Z}_{+},$ we construct an $A_{g,n}(V)$-bimodule $Å_{g,n}(M)$ and study its some properties, discuss the connections between bimodule $Å_{g,n}(M)$ and intertwining operators. Especially, bimodule $Å_{g,n-\frac{1}{T}}(M)$ is a natural quotient of $Å_{g,n}(M)$ and there is a linear isomorphism between the space ${\cal I}_{M\,M^j}^{M^k}$ of intertwining operators and the space of homomorphisms $\rm{Hom}_{A_{g,n}(V)}(Å_{g,n}(M)\otimes_{A_{g,n}(V)}M^j(s), M^k(t))$ for $s,t\leq n, M^j, M^k$ are $g$-twisted $V$ modules, if $V$ is $g$-rational.

math.RT↗

arXiv2013

Fusion rules for the vertex operator algebra $V_{L_{2}}^{A_{4}}$

The fusion rules for vertex operator algebra $V_{L_{2}}^{A_{4}}$ are determined.

math.QA↗

arXiv2012

Mirror Extensions of Vertex Operator Algebras

The mirror extensions for vertex operator algebras are studied. Two explicit examples which are not simple current extensions of some affine vertex operator algebras of type $A$ are given.

math.QA↗

arXiv2012

Quantum Dimensions and Quantum Galois Theory

The quantum dimensions of modules for vertex operator algebras are defined and their properties are discussed. The possible values of the quantum dimensions are obtained for rational vertex operator algebras. A criterion for simple currents of a rational vertex operator algebra is given. A full Galois theory for rational vertex operator algebras is established using the quantum dimensions.

math.QA↗