arXiv subjects

Hongyan Guo

Publications and source records attributed to Hongyan Guo.

16 recordsLinked to original sources

arXiv2026

On integral forms for vertex superalgebras associated with affine Lie superalgebras and their modules

This paper studies integral forms for affine vertex superalgebras and their modules. We first obtain integral forms for the universal enveloping superalgebra $U(\hat{\g})$ of an affine Lie superalgebra $\hat{\g}$. For $\g$ a basic classical Lie superalgebra, we give another construction of integral forms for $U(\hat{\g})$ using Chevalley basis, generalizing Kostant-Garland integral form theory. Then we apply the theory to construct integral forms for vertex (operator) superalgebras based on affine Lie superalgebras and their modules, we also investigate when an integral form contains the conformal vector, and integral forms in contragredient modules for vertex operator superalgebras.

math.QA↗

arXiv2023

Restricted modules and associated vertex algebras of extended Heisenberg-Virasoro algebra

In this paper, a family of infinite dimensional Lie algebras $\tilde{\mathcal{L}}$ is introduced and investigated, called the extended Heisenberg-Virasoro algebra,denoted by $\tilde{\mathcal{L}}$. These Lie algebras are related to the $N=2$ superconformal algebra and the Bershadsky-Polyakov algebra. We study restricted modules and associated vertex algebras of the Lie algebra $\tilde{\mathcal{L}}$. More precisely, we construct its associated vertex (operator) algebras $V_{\tilde{\mathcal{L}}}(\ell_{123},0)$, and show that the category of vertex algebra $V_{\tilde{\mathcal{L}}}(\ell_{123},0)$-modules is equivalent to the category of restricted $\tilde{\mathcal{L}}$-modules of level $\ell_{123}$.Then we give uniform constructions of simple restricted $\tilde{\mathcal{L}}$-modules. Also, we present several equivalent characterizations of simple restricted modules over $\tilde{\mathcal{L}}$.

math.RT↗

arXiv2022

Trigonometric Lie algebras, affine Kac-Moody Lie algebras, and equivariant quasi modules for vertex algebras

In this paper, we study a family of infinite-dimensional Lie algebras $\widehat{X}_{S}$, where $X$ stands for the type: $A,B,C,D$, and $S$ is an abelian group, which generalize the $A,B,C,D$ series of trigonometric Lie algebras. Among the main results, we identify $\widehat{X}_{S}$ with what are called the covariant algebras of the affine Lie algebra $\widehat{\mathcal{L}_{S}}$ with respect to some automorphism groups, where $\mathcal{L}_{S}$ is an explicitly defined associative algebra viewed as a Lie algebra. We then show that restricted $\widehat{X}_{S}$-modules of level $\ell$ naturally correspond to equivariant quasi modules for affine vertex algebras related to $\mathcal{L}_{S}$. Furthermore, for any finite cyclic group $S$, we completely determine the structures of these four families of Lie algebras, showing that they are essentially affine Kac-Moody Lie algebras of certain types.

math.QA↗

arXiv2022

Ultra-High Lithium Storage Capacity of Al2C Monolayer under Restricted Multilayered Growth Mechanism

Designing anode materials with high lithium specific capacity is crucial to the development of high energy-density lithium ion batteries. Herein, a distinctive lithium growth mechanism, namely, the restricted multilayered growth for lithium, and a strategy for lithium storage are proposed to achieve the balance between the ultra-high specific capacity and the need to avert uncontrolled dendritic growth of lithium. In particular, based on first-principles computation, we show that the Al2C monolayer with planar tetracoordinate carbon structure can be an ideal platform for realizing the restricted multilayered growth mechanism as a 2D anode material. Furthermore, the Al2C monolayer exhibits ultra-high specific capacity of lithium of 4059 mAh/g, yet with a low dif-fusion barrier of 0.039-0.17 eV as well as low open circuit voltage in the range of 0.002-0.34 V. These novel properties endow the Al2C monolayer a promising anode material for future lithium ion batteries. Our study offers a new way to design promising 2D anode materials with high specific capacity, fast lithium-ion diffusion, and safe lithium storage mechanism.

cond-mat.mtrl-sci↗

arXiv2022

Anisotropic Electrene T'-Ca2P with Electron Gas Magnetic Coupling as Anode Material for Na/K Ion Batteries

There is an urgently need for the high-performance rechargeable electrical storage devices as supplement or substitutions of lithium ion batteries due to the shortage of lithium in nature. Herein we propose a stable 2D electrene T'-Ca2P as anode material for Na/K ion batteries by first-principle calculations. Our calculated results show that T'-Ca2P monolayer is an antiferromagnetic semiconducting electrene with spin-polarized electron gas. It exhibits suitable adsorption for both Na and K atoms, and its anisotropic migration energy barriers are 0.050/0.101 eV and 0.037/0.091 eV in b/a direction, respectively. The theoretical capacities for Na and K are both 482 mAh/g, while the average working voltage platforms are 0.171-0.226 V and 0.013-0.267 V, respectively. All the results reveal that the T'-Ca2P monolayer has promised application prospects as anode materials for Na/K ion batteries.

cond-mat.mtrl-sci↗

arXiv2022

Restricted modules for gap-$p$ Virasoro algebra and twisted modules for certain vertex algebras

This paper studies restricted modules of gap-$p$ Virasoro algebra $Ł$ and their intrinsic connection to twisted modules of certain vertex algebras. We first establish an equivalence between the category of restricted $Ł$-modules of level $\el$ and the category of twisted modules of vertex algebra $V_{\mathcal{N}_{p}}(\el,0)$, where $\mathcal{N}_{p}$ is a new Lie algebra, $\el:=(\ell_{0},0,\cdots,0)\in\C^{\halfp+1}$, $\ell_{0}\in\C$ is the action of the Virasoro center. Then we focus on the construction and classification of simple restricted $Ł$-modules of level $\el$. More explicitly, we give a uniform construction of simple restricted $Ł$-modules as induced modules. We present several equivalent characterizations of simple restricted $Ł$-modules, as locally nilpotent (equivalently, locally finite) modules with respect to certain positive part of $Ł$. Moreover, simple restricted $Ł$-modules of level $\el$ are classified. They are either highest weight modules or simple induced modules. At the end, we exhibit several concrete examples of simple restricted $Ł$-modules of level $\el$ (including Whittaker modules).

math.RT↗

arXiv2021

Algebra of q-difference operators, affine vertex algebras, and their modules

In this paper, we explore a canonical connection between the algebra of $q$-difference operators $\widetilde{V}_{q}$, affine Lie algebra and affine vertex algebras associated to certain subalgebra $\mathcal{A}$ of the Lie algebra $\mathfrak{gl}_{\infty}$. We also introduce and study a category $\mathcal{O}$ of $\widetilde{V}_{q}$-modules. More precisely, we obtain a realization of $\widetilde{V}_{q}$ as a covariant algebra of the affine Lie algebra $\widehat{\mathcal{A}^{*}}$, where $\mathcal{A}^{*}$ is a 1-dimensional central extension of $\mathcal{A}$. We prove that restricted $\widetilde{V_{q}}$-modules of level $\ell_{12}$ correspond to $\mathbb{Z}$-equivariant $ϕ$-coordinated quasi-modules for the vertex algebra $V_{\widetilde{\mathcal{A}}}(\ell_{12},0)$, where $\widetilde{\mathcal{A}}$ is a generalized affine Lie algebra of $\mathcal{A}$. In the end, we show that objects in the category $\mathcal{O}$ are restricted $\widetilde{V_{q}}$-modules, and we classify simple modules in the category $\mathcal{O}$.

math.QA↗

arXiv2020

Automorphism group and twisted modules of the twisted Heisenberg-Virasoro vertex operator algebra

We first determine the automorphism group of the twisted Heisenberg-Virasoro vertex operator algebra $V_{\mathcal{L}}(\ell_{123},0)$.Then, for any integer $t>1$, we introduce a new Lie algebra $\mathcal{L}_{t}$, and show that $σ_{t}$-twisted $V_{\mathcal{L}}(\ell_{123},0)$($\ell_{2}=0$)-modules are in one-to-one correspondence with restricted $\mathcal{L}_{t}$-modules of level $\ell_{13}$, where $σ_{t}$ is an order $t$ automorphism of $V_{\mathcal{L}}(\ell_{123},0)$. At the end, we give a complete list of irreducible $σ_{t}$-twisted $V_{\mathcal{L}}(\ell_{123},0)$($\ell_{2}=0$)-modules.

math.QA↗

arXiv2018

A New Two-Dimensional Functional Material with Desirable Bandgap and Ultrahigh Carrier Mobility

Two-dimensional (2D) semiconductors with direct and modest bandgap and ultrahigh carrier mobility are highly desired functional materials for nanoelectronic applications. Herein, we predict that monolayer CaP3 is a new 2D functional material that possesses not only a direct bandgap of 1.15 eV (based on HSE06 computation), and also a very high electron mobility up to 19930 cm2 V-1 s-1, comparable to that of monolayer phosphorene. More remarkably, contrary to the bilayer phosphorene which possesses dramatically reduced carrier mobility compared to its monolayer counterpart, CaP3 bilayer possesses even higher electron mobility (22380 cm2 V-1 s-1) than its monolayer counterpart. The bandgap of 2D CaP3 can be tuned over a wide range from 1.15 to 0.37 eV (HSE06 values) through controlling the number of stacked CaP3 layers. Besides novel electronic properties, 2D CaP3 also exhibits optical absorption over the entire visible-light range. The combined novel electronic, charge mobility, and optical properties render 2D CaP3 an exciting functional material for future nanoelectronic and optoelectronic applications.

cond-mat.mtrl-sci↗

arXiv2017

q-Virasoro algebra and affine Kac-Moody Lie algebras

We establish a natural connection of the $q$-Virasoro algebra $D_{q}$ introduced by Belov and Chaltikian with affine Kac-Moody Lie algebras. More specifically, for each abelian group $S$ together with a one-to-one linear character $χ$, we define an infinite-dimensional Lie algebra $D_{S}$ which reduces to $D_{q}$ when $S=\mathbb{Z}$. Guided by the theory of equivariant quasi modules for vertex algebras, we introduce another Lie algebra ${\mathfrak{g}}_{S}$ with $S$ as an automorphism group and we prove that $D_{S}$ is isomorphic to the $S$-covariant algebra of the affine Lie algebra $\widehat{\mathfrak{g}_{S}}$. We then relate restricted $D_{S}$-modules of level $\ell\in \mathbb{C}$ to equivariant quasi modules for the vertex algebra $V_{\widehat{\mathfrak{g}_{S}}}(\ell,0)$ associated to $\widehat{\mathfrak{g}_{S}}$ with level $\ell$. Furthermore, we show that if $S$ is a finite abelian group of order $2l+1$, $D_{S}$ is isomorphic to the affine Kac-Moody algebra of type $B^{(1)}_{l}$.

math.QA↗

arXiv2016

Twisted Heisenberg-Virasoro vertex operator algebra

In this paper, we study a new kind of vertex operator algebra related to the twisted Heisenberg-Virasoro algebra, which we call the twisted Heisenberg-Virasoro vertex operator algebra, and its modules. Specifically, we present some results concerning the relationship between the restricted module categories of twisted Heisenberg-Virasoro algebras of rank one and rank two and several different kinds of module categories of their corresponding vertex algebras. We also study fully the structures of the twisted Heisenberg-Virasoro vertex operator algebra, give a characterization of it as a tensor product of two well-known vertex operator algebras, and solve the commutant problem.

math.QA↗

arXiv2014

Phosphorene nanoribbons, nanotubes and van der Waals multilayers

We perform a comprehensive first-principles study of the electronic properties of phosphorene nanoribbons, phosphorene nanotubes, multilayer phosphorene, and heterobilayers of phosphorene and two-dimensional (2D) transition metal dichalcogenide (TMDC) monolayer. The tensile strain and electric-field effects on electronic properties of low-dimensional phosphorene nanostructures are also investigated. Our calculations show that zigzag phosphorene nanoribbons (z-PNRs) are metals, regardless of the ribbon width while armchair phosphorene nanoribbons (a-PNRs) are semiconductors with indirect bandgaps and the bandgaps are insensitive to variation of the ribbon width. We find that tensile compression (or expansion) strains can reduce (or increase) the bandgap of the a-PNRs while an in-plane electric field can significantly reduce the bandgap of a-PNRs, leading to the semiconductor-to-metal transition beyond certain electric field. For single-walled phosphorene nanotubes (SW-PNTs), both armchair and zigzag nanotubes are semiconductors with direct bandgaps. With either tensile strains or transverse electric field, similar behavior of bandgap modulation can arise as that for a-PNRs. It is known that multilayer phosphorene sheets are semiconductors with their bandgaps decreasing with increasing the number of multilayers. In the presence of a vertical electric field, the bandgaps of multilayer phosphorene sheets decrease with increasing the electric field, and the bandgap modulation is more significant with more layers. Lastly, heterobilayers of phosporene with a TMDC (MoS2 or WS2) monolayer are still semiconductors while their bandgaps can be reduced by applying a vertical electric field as well.

cond-mat.mes-hall↗

arXiv2014

Tuning Electronic and Magnetic Properties of Early Transition Metal Dichalcogenides via Tensile Strain

We have performed a systematic first-principles study of the effect of tensile strains on the electronic properties of early transition-metal dichalcogenide (TMDC) monolayers MX2 (M = Sc, Ti, Zr, Hf, Ta, Cr; X = S, Se, and Te). Our density-functional theory (DFT) calculations suggest that the tensile strain can significantly affect the electronic properties of many early TMDCs in general and the electronic bandgap in particular. For group IVB TMDCs (TiX2, ZrX2, HfX2), the bandgap increases with the tensile strain, but for ZrX2 and HfX2 (X=S, Se), the bandgap starts to decrease at strain 6% to 8%. For the group-VB TMDCs (TaX2), the tensile strain can either induce the ferromagnetism or enhance the existing ferromagnetism. For the group-VIB TMDCs (CrX2) the direct-to-indirect bandgap transition is seen upon application of the tensile strain, except CrTe2 whose bandgap decreases with the tensile strain even though the direct character of its bandgap is retained. Lastly, for the group-IIIB TMDCs (ScX2) in the T metallic phase, we find that the tensile strain has little effect on their electronic and magnetic properties. Our study suggests that strain engineering is an effective approach to modify electronic and magnetic properties of most early TMDC monolayers, thereby opening an alternative way for future optoelectronic and spintronic applications.

cond-mat.mes-hall↗

arXiv2014

$q$-Virasoro algebra and vertex algebras

In this paper, we study a certain deformation $D$ of the Virasoro algebra that was introduced and called $q$-Virasoro algebra by Nigro,in the context of vertex algebras. Among the main results, we prove that for any complex number $\ell$, the category of restricted $D$-modules of level $\ell$ is canonically isomorphic to the category of quasi modules for a certain vertex algebra of affine type. We also prove that the category of restricted $D$-modules of level $\ell$ is canonically isomorphic to the category of $\mathbb{Z}$-equivariant $ϕ$-coordinated quasi modules for the same vertex algebra. In the process, we introduce and employ a certain infinite dimensional Lie algebra which is defined in terms of generators and relations and then identified explicitly with a subalgebra of $\mathfrak{gl}_{\infty}$.

math.QA↗

arXiv2013

MoS2/MX2 heterobilayers: Bandgap engineering via tensile strain or external electrical field

We have performed a comprehensive first-principles study of the electronic and magnetic properties of two-dimensional (2D) transition-metal dichalcogenide (TMD) heterobilayers MX2/MoS2 (M = Mo, Cr, W, Fe, V; X = S, Se). For M = Mo, Cr, W; X=S, Se, all heterobilayers show semiconducting characteristics with an indirect bandgap with the exception of the WSe2/MoS2 heterobilayer which retains the direct-band-gap character of the constituent monolayer. For M = Fe, V; X = S, Se, the MX2/MoS2 heterobilayers exhibit metallic characters. Particular attention of this study has been focused on engineering bandgap of the TMD heterobilayer materials via application of either a tensile strain or an external electric field. We find that with increasing either the biaxial or uniaxial tensile strain, the MX2/MoS2 (M=Mo, Cr, W; X=S, Se) heterobilayers can undergo a semiconductor-to-metal transition. For the WSe2/MoS2 heterobilayer, a direct-to-indirect bandgap transition may occur beyond a critical biaxial or uniaxial strain. For M (=Fe, V) and X (=S, Se), the magnetic moments of both metal and chalcogen atoms are enhanced when the MX2/MoS2 heterobilayers are under a biaxial tensile strain. Moreover, the bandgap of MX2/MoS2 (M=Mo, Cr, W; X=S, Se) heterobilayers can be reduced by the electric field. For two heterobilayers MSe2/MoS2 (M=Mo, Cr), PBE calculations suggest that the indirect-to-direct bandgap transition may occur under an external electric field. The transition is attributed to the enhanced spontaneous polarization. The tunable bandgaps in general and possible indirect-direct bandgap transitions due to tensile strain or external electric field endow the TMD heterobilayer materials a viable candidate for optoelectronic applications.

cond-mat.mes-hall↗

arXiv2013

Some categories of modules for toroidal Lie algebras

In this paper, we use basic formal variable techniques to study certain categories of modules for the toroidal Lie algebra $τ$. More specifically, we define and study two categories $\mathcal{E}_τ$ and $\mathcal{C}_τ$ of $τ$-modules using generating functions, where $\mathcal{E}_τ$ is proved to contain the evaluation modules while $\mathcal{C}_τ$ contains certain restricted $τ$-modules, the evaluation modules, and their tensor product modules. Furthermore, we classify the irreducible integrable modules in categories $\mathcal{E}_τ$ and $\mathcal{C}_τ$.

math.RT↗