Searcharxiv⌕ Search

arXiv subjects

Zhiqiang Yu

Publications and source records attributed to Zhiqiang Yu.

16 recordsLinked to original sources
arXiv2026

Classification of some $\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z}$-quadratic fusion categories of rank 6

A fusion category $\mathcal{C}$ is said to be $\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z}$-quadratic if the group $G(\mathcal{C})$ of invertible objects is isomorphic to $\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z}$, and the remaining simple objects form an orbit under the action of $G(\mathcal{C})$. In this paper, we give a partial classification of $\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z}$-quadratic fusion categories of rank six. More precisely, we show that its Grothendieck ring $\mathcal{K}_0(\mathcal{C})$ must be one of nine fusion rings if the fusion rule multiplicities are less than $20$, and the categorifications of five of them are previously known. We prove that one of the last four fusion rings can be realized as de-equivariantization of a near-group fusion category of type $\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/4\mathbb{Z}+8$.

math.QA↗
arXiv2026

On the structure of Witt groups and minimal extension conjecture

Let $\mathcal{E}=\text{Rep}(G)$ be a Tannakian fusion category. For a braided fusion category $\mathcal{C}$ over $\mathcal{E}$ we give sufficient and necessary conditions that characterize the Witt relation $[\mathcal{C}]=[\mathcal{E}]$. Then we show the Witt group $\mathcal{W}(\mathcal{E})$ is naturally a direct sum of Witt group $\mathcal{W}:=\mathcal{W}(\text{Vec})$ and the group $\text{H}^4(G,\mathbb{K}^\times)$. Consequently, for any non-degenerate fusion category $\mathcal{C}$ over $\mathcal{E}$, there is a positive integer $n$ (e.g. $n=|G|$) such that $\mathcal{C}^{\boxtimes_\mathcal{E}^n}$ admits a minimal extension.

math.CT↗
arXiv2025

On the Casimir number and formal codegree of Haagerup-Izumi fusion rings

For any cyclic group $\mathbb{Z}_n$, we first determine the Casimir number and determinant of the Haagerup-Izumi fusion ring $\mathcal{HI}_{\mathbb{Z}_n}$, it turns out that they do not share the same set of prime factors. Then we show that all finite-dimensional irreducible representations of $\mathcal{HI}_{\mathbb{Z}_n}$ are defined over certain cyclotomic fields. As a direct result, we obtain the formal codegrees of $\mathcal{HI}_{\mathbb{Z}_n}$, which satisfy the pseudo-unitary inequality.

math.QA↗
arXiv2024

Realizing modular data from centers of near-group categories

In this paper, we show the existence of a near-group category of type $\mathbb{Z} / 4\mathbb{Z} \times \mathbb{Z} / 4\mathbb{Z}+16$ and compute the modular data of its Drinfeld center. We prove that a modular data of rank $10$ can be obtained through condensation of the Drinfeld center of the near-group category $\mathbb{Z} / 4\mathbb{Z} \times \mathbb{Z} / 4\mathbb{Z}+16$, and it can also be realized as the Drinfeld center of a fusion category of rank $4$. Moreover, we compute the modular data for the Drinfeld center of a near-group category $\mathbb{Z} / 8\mathbb{Z}+8$ and show that the non-pointed factor of its condensation has the same modular data as the quantum group category $C(\mathfrak{g}_2, 4)$.

math.QA↗
arXiv2023

On the center of near-group fusion category of type $\mathbb{Z}_3+6$

Let $\mathcal{A}$ be a near-group fusion category of type $\mathbb{Z}_3+6$. We show that there is a modular tensor equivalence $\mathcal{Z}(\mathcal{A})\cong\mathcal{C}(\mathbb{Z}_3,\eta)\boxtimes\mathcal{C}(\mathfrak{sl}_3,9)_{\mathbb{Z}_3}^0$. Moreover, we construct two non-trivial faithful extensions of $\mathcal{A}$ explicitly, whose Drinfeld centers can also be obtained from representation categories quantum groups at root of unity.

math.QA↗
arXiv2023

On the realization of a class of $\text{SL}(2,\mathbb{Z})$-representations

Let $p<q$ be odd primes, $\rho_1$ and $\rho_2$ be irreducible representations of $\text{SL}(2,\mathbb{Z}_p)$ and $\text{SL}(2,\mathbb{Z}_q)$ of dimensions $\frac{p+1}{2}$ and $\frac{q+1}{2}$, respectively. We show that if $\rho_1\oplus\rho_2$ can be realized as modular representation associated to a modular fusion category $\mathcal{C}$, then $q-p=4$. Moreover, if $\mathcal{C}$ contains a non-trivial \'{e}tale algebra, then $\mathcal{C}\boxtimes\mathcal{C}(\mathbb{Z}_p,\eta)\cong\mathcal{Z}(\mathcal{A})$ as braided fusion category, where $\mathcal{A}$ is a near-group fusion category of type $(\mathbb{Z}_p,p)$. And we show that there exists a non-trivial $\mathbb{Z}_2$-extension of $\mathcal{A}$ that contains simple objects of Frobenius-Perron dimension $\frac{\sqrt{p}+\sqrt{q}}{2}$.

math.QA↗
arXiv2022

Pre-modular fusion categories of global dimensions $p^2$

Let $p\geq5$ be a prime, we show that a non-pointed modular fusion category $\mathcal{C}$ is Grothendieck equivalent to $\mathcal{C}(\mathfrak{sl}_2,2(p-1))_A^0$ if and only if $\dim(\mathcal{C})=p\cdot u$, where $u$ is a certain totally positive algebraic unit and $A$ is the regular algebra of the Tannakian subcategory $\text{Rep}(\mathbb{Z}_2)\subseteq\mathcal{C}(\mathfrak{sl}_2,2(p-1))$. As a direct corollary, we classify non-simple modular fusion categories of global dimensions $p^2$.

math.QA↗
arXiv2021

Modular tensor categories, subcategories, and Galois orbits

We establish a set of general results to study how the Galois action on modular tensor categories interacts with fusion subcategories. This includes a characterization of fusion subcategories of modular tensor categories which are closed under the Galois action, and a classifcation of modular tensor categories which factor as a product of pointed and transitive categories in terms of pseudoinvertible objects. As an application, we classify modular tensor categories with two Galois orbits of simple objects and a nontrivial grading group.

math.QA↗
arXiv2021

On the minimal extension and structure of weakly group-theoretical braided fusion categories

We show that any slightly degenerate weakly group-theoretical fusion category admits a minimal non-degenerate extension. Let $d$ be a positive square-free integer, given a weakly group-theoretical non-degenerate fusion category $\mathcal{C}$, assume that $\text{FPdim}(\mathcal{C})=nd$ and $(n,d)=1$. If $(\text{FPdim}(X)^2,d)=1$ for all simple objects $X$ of $\mathcal{C}$, then we show that $\mathcal{C}$ contains a non-degenerate fusion subcategory $\mathcal{C}(\mathbb{Z}_d,q)$. In particular, we obtain that integral fusion categories of FP-dimensions $p^md$ such that $\mathcal{C}'\subseteq \text{sVec}$ are nilpotent and group-theoretical, where $p$ is a prime and $(p,d)=1$.

math.QA↗
arXiv2021

Pre-modular fusion categories of small global dimensions

We first prove an analogue of Lagrange theorem for global dimensions of fusion categories, then we give a complete classifications of pre-modular fusion categories of integer global dimensions less than or equal to $10$.

math.QA↗
arXiv2019

On slightly degenerate fusion categories

In this paper, we first show for a slightly degenerate pre-modular fusion category $\mathcal{C}$ that squares of dimensions of simple objects divide half of the dimension of $\mathcal{C}$, and that slightly degenerate fusion categories of FP-dimensions $2p^nd$ and $4p^nd$ are nilpotent, where $p$ is an odd prime and $d$ is an odd square-free integer. Then we classify slightly degenerate generalized Tambara-Yamagami fusion categories and weakly integral slightly degenerate fusion categories of particular dimensions.

math.QA↗
arXiv2019

Energy-dependent normal and unusually large inverse chlorine kinetic isotope effects of simple chlorohydrocarbons in collision-induced dissociation by gas chromatography-tandem mass spectrometry

Kinetic isotope effects (KIEs) taking place in mass spectrometry (MS) can provide in-depth insights into the fragmental behaviors of compounds in MS. Yet the mechanisms of KIEs in collision-induced dissociation (CID) in tandem MS are unclear, and information about chlorine KIEs (Cl-KIEs) of organochlorines in MS is particularly scarce. This study investigated the Cl-KIEs of dichloromethane, trichloroethylene and tetrachloroethylene during CID using gas chromatography-electron ionization triple-quadrupole tandem MS. Cl-KIEs were measured with MS signal intensities, and their validity was confirmed in terms of chromatograms, crosstalk effects and background subtraction influences. All the organochlorines presented large inverse Cl-KIEs, showing the largest values of 0.492, 0.910 and 0.892 at the highest collision energy for dichloromethane, trichloroethylene and tetrachloroethylene, respectively. For dichloromethane, both intra-ion and inter-ion Cl-KIEs were studied, within the ranges of 0.492-1.020 and 0.614-1.026, respectively, showing both normal and inverse Cl-KIEs depending on collision energies. The observed Cl-KIEs generally declined with the increasing collision energies from 0-60 eV, but were inferred to be independent of MS signal intensities. The Cl-KIEs are dominated by critical energies at low internal energies, while controlled by rotational barriers (or looseness/tightness of transition states) at high internal energies. It is concluded that the Cl-KIEs may depend on critical energies, bond strengths, available internal energies, and transition state looseness/tightness. The findings of this study yield new insights into the fundamentals of Cl-KIEs of organochlorines during CID, and may be conducive to elucidating the mechanisms of KIEs in collision-induced and photo-induced reactions in the actual world.

physics.chem-ph↗
arXiv2017

Categorical Morita equivalence and monoidal Morita equivalence of semisimple Hopf algebras of dimension pqr

In this paper, we determine the cocycle deformations and Galois objects for semisimple Hopf algebras of dimension pqr, and decide the categorically Morita equivalent classes and monoidally Morita equivalent classes of them. We show that all of them only have one trivial Galois objects, therefore these Hopf algebras are pairwise twist inequivalent, equivalently they are not monoidally Morita equivalent to each other, moreover, all the categorically Morita equivalent classes are determined.

math.RT↗
arXiv2017

Cocycle deformations and Galois objects of semisimple Hopf algebras of dimension $16$

In this article, we determine cocycle deformations and Galois objects of non-commutative and non-cocommutative semisimple Hopf algebras of dimension $16$. We show that these Hopf algebras are pairwise twist inequivalent mainly by calculating their higher Frobenius-Schur indicators, and that except three Hopf algebras which are cocycle deformations of dual group algebras, none of them admit non-trivial cocycle deformations.

math.RT↗
arXiv2016

Very Long-period Pulsations before the Onset of Solar Flares

Solar flares are the most powerful explosions occurring in the solar system, which may lead to disastrous space weather events and impact various aspects of our Earth. So far, it is still a big challenge in modern astrophysics to understand the origin of solar flares and predict their onset. Based on the analysis of soft X-ray emission observed by the Geostationary Operational Environmental Satellite (GOES), this work reported a new discovery of very long-periodic pulsations occurred in the preflare phase before the onset of solar flares (preflare-VLPs). These pulsations are typically with period of 8 - 30 min and last for about 1 - 2 hours. They are possibly generated from LRC oscillations of plasma loops where electric current dominates the physical process during magnetic energy accumulation in the source region. The preflare-VLP provides an essential information for understanding the triggering mechanism and origin of solar flares, and may help us to response to solar explosions and the corresponding disastrous space weather events as a convenient precursory indicator.

astro-ph.SR↗