论文标题
编织的霍普夫代数和仪表转换
Braided Hopf algebras and gauge transformations
论文作者
论文摘要
我们研究了均质的非交换主束的无限规变量，作为派生的编织代数。为此，我们分析了$ k $编织的Hopf和Lie代数，以$ k $ a（quasi）三角形的霍夫夫代数为symmorties，并将其作为编织派生的代表。然后，我们研究编织的Hopf代数的Drinfeld扭曲变形和无穷小规变量的代数。我们给出了来自阿贝利安和约旦类型的变形的例子。特别是，我们明确描述了Instanton捆绑包和量子束的量规变换的编织谎言代数。
We study infinitesimal gauge transformations of an equivariant noncommutative principal bundle as a braided Lie algebra of derivations. For this, we analyse general $K$-braided Hopf and Lie algebras, for $K$ a (quasi)triangular Hopf algebra of symmetries, and study their representations as braided derivations. We then study Drinfeld twist deformations of braided Hopf algebras and of Lie algebras of infinitesimal gauge transformations. We give examples coming from deformations of abelian and Jordanian type. In particular we explicitly describe the braided Lie algebra of gauge transformations of the instanton bundle and of the orthogonal bundle on the quantum sphere $S^4_θ$.
