arXiv subjects

Jinrong Wang

Publications and source records attributed to Jinrong Wang.

3 recordsLinked to original sources

arXiv2026

Simple restricted modules over a new Lie superalgebra extended by the Ovsienko--Roger algebra

In this paper, we introduce a new infinite-dimensional Lie superalgebra $\mathcal{S}$ called the super extended Ovsienko--Roger algebra. This algebra is obtained by determining the annihilation superalgebra of the Lie conformal superalgebra $S=S_{\bar0}\oplus S_{\bar{1}}$ with $S_{\bar{0}}=\mathbb{C}[\partial]L\oplus\mathbb{C}[\partial]W$, $S_{\bar{1}}=\mathbb{C}[\partial]G$ and non-trivial $λ$-brackets $[L_λL]=(\partial+2λ)L$, $[L_λG]=(\partial+λ)G$, $[L_λW]=[G_λG]=\partial W$. Then we construct a class of simple restricted $\mathcal{S}$-modules, which are induced from simple modules of some finite dimensional solvable Lie superalgebras under certain conditions. Moreover, we obtain the classification of simple generalized Verma modules over $\mathcal{S}$ and we show that the Verma module of $\mathcal{S}$ is always reducible.

math.RT↗

arXiv2025

Lie conformal superalgebras of rank (2 + 1)

In this paper, Lie conformal superalgebras of rank (2 + 1) are completely classified (up to isomorphism) and their automorphism groups are determined. Furthermore, we give the classification of the finite irreducible conformal modules over them and the actions are explicitly described.

math.RA↗

arXiv2024

Two classes of Lie conformal superalgebras related to the Heisenberg--Virasoro Lie conformal algebra

In this paper, firstly we construct two classes of Lie conformal superalgebras denoted by $\mathcal{HVS}(α)$ and $\mathcal{HVS}(β,γ,τ)$, respectively, where $α$ is an nonzero complex number and $β,γ,τ$ are complex numbers. They are both of rank $(2+1)$ and the even part $\mathcal{HVS}(α)_{\bar{0}}=\mathcal{HVS}(β,γ,τ)_{\bar{0}}$ is the Heisenberg--Virasoro Lie conformal algebra, which is a free $\mathbb{C}[\partial]$-module generated by $L$ and $H$ satisfying $[L_λL]=(\partial+2λ)L,\ [L_λH]=(\partial+λ)H,\ [H_λH]=0$. Then we completely determine the conformal derivations, conformal biderivations, automorphism groups and conformal modules of rank $(1+1)$ for these two Lie conformal superalgebras.

math.RA↗