路子余代数、有限性与量子群
Path subcoalgebras, finiteness properties and quantum groups
摘要：
研究了由路所张成的路余代数的子余代数（称为路子余代数）和关联余代数的子余代数，并给出了这两类子余代数的统一方法。我们讨论了这些余代数的左拟余Frobenius和左余Frobenius性质。我们对左余弗罗贝纽斯路子余代数进行了分类，证明它们是由无限线箭图或循环箭图产生的某些路子余代数的直和。我们还讨论了所考虑的余代数类的余自反性质。最后，我们研究了余Frobenius路子余代数中的哪一个可以被赋予霍普夫代数结构，以产生具有非零积分的量子群，并对具有任意阶单位原根的域上的所有这些结构进行了分类.这些结果是量子线在某些不一定是阿贝尔群上的提升。
英文摘要：
We study subcoalgebras of path coalgebras that are spanned by paths (called path subcoalgebras) and subcoalgebras of incidence coalgebras, and propose a unifying approach for these classes. We discuss the left quasi-co-Frobenius and the left co-Frobenius properties for these coalgebras. We classify the left co-Frobenius path subcoalgebras, showing that they are direct sums of certain path subcoalgebras arising from the infinite line quiver or from cyclic quivers. We also discuss the coreflexive property for the considered classes of coalgebras. Finally, we investigate which of the co-Frobenius path subcoalgebras can be endowed with Hopf algebra structures, in order to produce some quantum groups with non-zero integrals, and classify all these structures over a field with primitive roots of unity of any order. These turn out to be liftings of quantum lines over certain not necessarily abelian groups.
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