论文标题
基本的HOPF代数和对称双模型
Basic Hopf algebras and symmetric bimodules
论文作者
论文摘要
由所谓的H细胞还原定理的动机，我们研究了某些类别的生物学类别，这些生物与可能只有一个H细胞。我们表明，具有唯一H细胞H_0的H_0-simple Quasi fiab bicateGories是融合类别。我们进一步研究了两类非偏squasi-fiab bicategories，除了身份外，具有单个H细胞。第一个是$ \ ch_a $，由有限尺寸分级的基本Hopf代数A索引，第二个是$ \ cg_a $，由对称的投影型A-A-A-Bimodules组成。我们表明，$ \ ch_a $可以看作是$ \ cg_a $的1-满足subbicateGory，并对$ \ cg_a $进行分类简单的瞬态birepresentations。我们指出，后者的等价类的数量是有限的，而对于$ \ ch_a $，通常不是。
Motivated by the so-called H-cell reduction theorems, we investigate certain classes of bicategories which have only one H-cell apart from possibly the identity. We show that H_0-simple quasi fiab bicategories with unique H-cell H_0 are fusion categories. We further study two classes of non-semisimple quasi-fiab bicategories with a single H-cell apart from the identity. The first is $\cH_A$, indexed by a finite-dimensional radically graded basic Hopf algebra A, and the second is $\cG_A$, consisting of symmetric projective A-A-bimodules. We show that $\cH_A$ can be viewed as a 1-full subbicategory of $\cG_A$ and classify simple transitive birepresentations for $\cG_A$. We point out that the number of equivalence classes of the latter is finite, while that for $\cH_A$ is generally not.
