标题： $(d,σ)$-扭曲仿射-维拉索罗超代数 显示英文标题

标题： $(d,σ)$-twisted Affine-Virasoro superalgebras

摘要： 对于任意有限维李超代数$\dot{\mathfrak{g}}$（可能是李代数），带有偶导子$d$和一个与$d$可交换的有限阶自同构$\sigma$，我们引入了$(d,\sigma)$-扭曲仿射-维拉索超代数$\mathfrak{L}=\mathfrak{L}(\dot{\mathfrak{g}},d,\sigma)$并确定了其万有中心扩张$\hat{\mathfrak{L}}=\hat{\mathfrak{L}}(\dot{\mathfrak{g}},d,\sigma)$。 这是一个无限维李超代数的巨大类。 这类李超代数包括许多新的和已知的李代数和超代数，包括仿射-维拉索罗超代数、扭曲的海森堡-维拉索罗代数、镜像海森堡-维拉索罗代数、W-代数$W(2,2)$、间隙-$p$维拉索罗代数、费米子-维拉索罗代数、$N=1$BMS 超代数、平面伽利略共形代数。 然后我们通过从$U(\mathfrak{h})$-自由模到权模的加权函子，给出了尖点$A\mathfrak{L}$-模的分类。 因此，我们通过$A$-覆盖方法给出了简单尖点$\mathfrak{L}$-模的分类。 最后，所有关于$\mathfrak{L}$和$\hat{\mathfrak{L}}$的简单拟有限模都被分类。 我们的结果恢复了数学和数学物理中许多已知的李超代数结果，并给出了许多新的李超代数。 显示英文摘要

摘要： For any finite dimensional Lie superalgebra $\dot{\mathfrak{g}}$ (maybe a Lie algebra) with an even derivation $d$ and a finite order automorphism $\sigma$ that commutes with $d$, we introduce the $(d,\sigma)$-twisted Affine-Virasoro superalgebra $\mathfrak{L}=\mathfrak{L}(\dot{\mathfrak{g}},d,\sigma)$ and determine its universal central extension $\hat{\mathfrak{L}}=\hat{\mathfrak{L}}(\dot{\mathfrak{g}},d,\sigma)$. This is a huge class of infinite-dimensional Lie superalgebras. Such Lie superalgebras consist of many new and well-known Lie algebras and superalgebras, including the Affine-Virasoro superalgebras, the twisted Heisenberg-Virasoro algebra, the mirror Heisenberg-Virasoro algebra, the W-algebra $W(2,2)$, the gap-$p$ Virasoro algebras, the Fermion-Virasoro algebra, the $N=1$ BMS superalgebra, the planar Galilean conformal algebra. Then we give the classification of cuspidal $A\mathfrak{L}$-modules by using the weighting functor from $U(\mathfrak{h})$-free modules to weight modules. Consequently, we give the classification of simple cuspidal $\mathfrak{L}$-modules by using the $A$-cover method. Finally, all simple quasi-finite modules over $\mathfrak{L}$ and $\hat{\mathfrak{L}}$ are classified. Our results recover many known Lie superalgebra results from mathematics and mathematical physics, and give many new Lie superalgebras.