标题： 节点三次曲线是一个量子齐次空间 显示英文标题

标题： The Nodal Cubic is a Quantum Homogeneous Space

摘要： 最近发现尖点可以赋予量子齐次空间的结构，即其坐标环$B$可以作为右余理想子代数嵌入到一个霍普夫代数$A$中，使得$A$作为$B$-模是忠实平坦的。 在本文中，为结点三次曲线的坐标环$B$构造了这样的霍普夫代数$A$，从而进一步激发了关于哪些仿射簇是量子齐次空间的问题。 还证明了$A$不是$B$的分裂扩张。 显示英文摘要

摘要： The cusp was recently shown to admit the structure of a quantum homogeneous space, that is, its coordinate ring $B$ can be embedded as a right coideal subalgebra into a Hopf algebra $A$ such that $A$ is faithfully flat as a $B$-module. In the present article such a Hopf algebra $A$ is constructed for the coordinate ring $B$ of the nodal cubic, thus further motivating the question which affine varieties are quantum homogeneous spaces. It is also shown that $A$ is not a cleft extension of $B$.