arXiv subjects
Publications and source records attributed to Yukun Xiao.
We determine all premodular subcategories and modular tensor subcategories in the module categories of Virasoro vertex operator algebras $L(c_{p,q},0)$ and the module categories of the simple current extensions of $L(c_{p,p+1},0)$.
Van der Waals (vdW) layered materials have gained significant attention owing to their distinctive structure and unique properties. The weak interlayer bonding in vdW layered materials enables guest atom intercalation, allowing precise tuning of their physical and chemical properties. In this work, a ternary compound, NixIn2Se3 (x = 0-0.3), with Ni randomly occupying the interlayers of In2Se3, was synthesized via an intercalation route driven by electron injection. The intercalated Ni atoms act as anchor points within the interlayer of In2Se3, which effectively suppresses the phase transition of In2Se3 at elevated temperatures. Furthermore, the disordered Ni intercalation significantly enhanced the electrical conductivity of In2Se3 through electron injection, while reducing the thermal conductivity due to the interlayer phonon scattering, leading to an improved thermoelectric performance. For instance, the thermoelectric figure of merit (ZT) of Ni0.3In2Se3 increased by 86% (in-plane) and 222% (out-of-plane) compared to In2Se3 at 500 oC. These findings not only provide an effective strategy to enhance the performance of layered thermoelectric materials, but also demonstrate the potential of intercalation chemistry for expanding the application scope of van der Waals (vdW) layered materials.
In this paper, we construct a large class of new simple modules over the twisted $N=2$ superconformal algebra. These new simple modules are restricted modules based on the simple modules over certain finite-dimensional solvable Lie superalgebras, including various versions of Whittaker modules. We elaborate that they are also the twisted modules for the universal $N=2$ superconformal vertex algebra. On the other hand, we give an explicit characterization of the simple restricted modules over the twisted $N=2$ superconformal algebra $\mathcal{T}$ under the condition that $T_t$ in $\mathcal{T}$ acts injectively for some $t\in \frac{1}{2}+\Z_+$.
In this paper, the structure of cocommutative vertex bialgebras is investigated. For a general vertex bialgebra $V$, it is proved that the set $G(V)$ of group-like elements is naturally an abelian semigroup, whereas the set $P(V)$ of primitive elements is a vertex Lie algebra. For $g\in G(V)$, denote by $V_g$ the connected component containing $g$. Among the main results, it is proved that if $V$ is a cocommutative vertex bialgebra, then $V=\oplus_{g\in G(V)}V_g$, where $V_{\bf 1}$ is a vertex subbialgebra which is isomorphic to the vertex bialgebra ${\mathcal{V}}_{P(V)}$ associated to the vertex Lie algebra $P(V)$, and $V_g$ is a $V_{\bf 1}$-module for $g\in G(V)$. In particular, this shows that every cocommutative connected vertex bialgebra $V$ is isomorphic to ${\mathcal{V}}_{P(V)}$ and hence establishes the equivalence between the category of cocommutative connected vertex bialgebras and the category of vertex Lie algebras. Furthermore, under the condition that $G(V)$ is a group and lies in the center of $V$, it is proved that $V={\mathcal{V}}_{P(V)}\otimes \C[G(V)]$ as a coalgebra where the vertex algebra structure is explicitly determined.