论文标题
Hochschild共同学，模块化张量类别和映射课程组
Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups
论文作者
论文摘要
给定有有限的模块化张量类别，我们将每个紧凑的表面与边界的双线轴复合物相关联，以使表面的映射类基团在其同胞组上进行投影作用。在零程度上，此动作与映射类组在手性结合块空间上的已知投影作用相吻合。在表面是圆环的情况下，类别是可分解的色带Hopf代数的表示类别，我们在模块化组对Hopf代数的Hochschild cohomology群体的投影作用上恢复了先前的结果。
Given a finite modular tensor category, we associate with each compact surface with boundary a cochain complex in such a way that the mapping class group of the surface acts projectively on its cohomology groups. In degree zero, this action coincides with the known projective action of the mapping class group on the space of chiral conformal blocks. In the case that the surface is a torus and the category is the representation category of a factorizable ribbon Hopf algebra, we recover our previous result on the projective action of the modular group on the Hochschild cohomology groups of the Hopf algebra.
