顶点（算子）代数的泛函解析理论，II
A functional-analytic theory of vertex (operator) algebras, II
摘要：
对中心电荷为c的有限生成顶点算子代数，构造了一个局部凸拓扑完备.在完备化的基础上，我们构造了具有有序解析参数化边界分量的亏格为零的Riemann曲面的模空间上的行列式线丛的c/2次方运算元上的代数结构.特别是，完成是一个模块的半群的c/2次幂的行列式线丛在模空间的共形等价类的annuli解析参数化的边界组件。第一部分中关于Z-分次顶点代数的结果也用框架小盘运算重新表述。利用May的双圈空间识别原理，这种运算公式的一个直接结果是：对应于第一部分和本文中构造的局部凸完备化的紧生成空间（或其k-化）具有双闭路空间的弱同伦类型.我们还将上述结果推广到局部分次限制共形顶点代数和模。
英文摘要：
For a finitely-generated vertex operator algebra of central charge c, a locally convex topological completion is constructed. We construct on the completion a structure of an algebra over the operad of the c/2-th power of the determinant line bundle over the moduli space of genus-zero Riemann surfaces with ordered analytically parametrized boundary components. In particular, the completion is a module for the semi-group of the c/2-th power of the determinant line bundle over the moduli space of conformal equivalence classes of annuli with analytically parametrized boundary components. The results in Part I for Z-graded vertex algebras are also reformulated in terms of the framed little disk operad. Using May's recognition principle for double loop spaces, one immediate consequence of such operadic formulations is that the compactly generated spaces corresponding to (or the k-ifications of) the locally convex completions constructed in Part I and in the present paper have the weak homotopy types of double loop spaces. We also generalize the results above to locally-grading-restricted conformal vertex algebras and to modules.
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