Let \(\mathcal {C}\) be a decomposable plane curve over an algebraically closed field k of characteristic 0. That is, \(\mathcal {C}\) is defined in k² by an equation of the form g(x) = f(y), where g and f are polynomials of degree at least two. We use this data to construct three affine pointed Hopf algebras, A(x, a, g), A(y, b, f) and A(g, f), in the first two of which g [resp. f ] are skew primitive central elements, with the third being a factor of the tensor product of the first two. We conjecture that A(g, f) contains the coordinate ring \(\mathcal {O}(\mathcal {C})\) of \(\mathcal {C}\) as a quantum homogeneous space, and prove this when each of g and f has degree at most five or is a power of the variable. We obtain many properties of these Hopf algebras, and show that, for small degrees, they are related to previously known algebras. For example, when g has degree three A(x, a, g) is a PBW deformation of the localisation at powers of a generator of the downup algebra A(− 1,− 1,0). The final section of the paper lists some questions for future work.

令\（\ mathcal {C} \）是特征为0的代数封闭场k上的可分解平面曲线。也就是说，\（\ mathcal {C} \）在k ^2中由形式为g（x）= f（y），其中g和f是次数至少为2的多项式。我们使用此数据构造三个仿射尖的Hopf代数A（x，a，g），A（y，b，f）和A（g，f），其中前两个g [resp。f ]是原始原始中心元素，第三个是前两个张量积的因数。我们猜想，甲（克，˚F）中包含坐标环\（\ mathcal {Ó}（\ mathcal {C}）\）的\（\ mathcal {C} \）作为量子均匀空间，并证明此当每个的克和˚F具有至多5度或可变的功率。我们获得了这些霍普夫代数的许多性质，并表明它们在较小程度上与先前已知的代数有关。例如，当g阶数为3 A（x，a，g）是向下代数A（-1，-1,0）的生成器的功率下的局域性PBW变形。本文的最后一部分列出了一些有关未来工作的问题。