论文标题
二维定向空间形式的Meromororphic开弦顶点代数和模块
Meromorphic open-string vertex algebras and modules over two-dimensional orientable space forms
论文作者
论文摘要
我们研究了二维Riemannian歧管上的Meromormormorphic开放弦顶顶点及其模块，这些歧管完整，连接，定位，以及恒定的截面曲率$ k \ neq 0 $。使用平行张量，我们明确确定了Meromororphic开放串线顶点代数的基础，其模块由Laplace-Beltrami操作员的特征函数生成，及其不可及的商。我们还研究了由最低的重量子空间产生的模块，满足了几何有趣的条件。结果表明，这种类型的每种不可还原模块都是由歧管上的某些（局部）特征功能生成的。对这种类型的模块进行了分类，该模块承认一系列有限长度的组成系列。特别是非常明显的是，如果每个组合因子都是由特征值$ p（p-1）k $生成的，则对于某些$ p \ in \ mathbb {z} _+$而言，该模块是完全还原的。
We study the meromorphic open-string vertex algebras and their modules over the two-dimensional Riemannian manifolds that are complete, connected, orientable, and of constant sectional curvature $K\neq 0$. Using the parallel tensors, we explicitly determine a basis for the meromorphic open-string vertex algebra, its modules generated by eigenfunctions of the Laplace-Beltrami operator, and their irreducible quotients. We also study the modules generated by lowest weight subspace satisfying a geometrically interesting condition. It is showed that every irreducible module of this type is generated by some (local) eigenfunction on the manifold. A classification is given for modules of this type admitting a composition series of finite length. In particular and remarkably, if every composition factor is generated by eigenfunctions of eigenvalue $p(p-1)K$ for some $p\in \mathbb{Z}_+$, then the module is completely reducible.
