论文标题
椭圆/过度的谎言组结构$ \ wp $函数
The Lie Group Structure of Elliptic/Hyperelliptic $\wp$ Functions
论文作者
论文摘要
我们考虑了椭圆/过度的$ \ wp $函数的概括性双重变换，直到第三属。对于一个属的情况，从代数加法公式中，我们推断出Weierstrass $ \ wp $函数具有SO（2,1）$ \ cong $ sp（2，$ \ r $）/$ \ z_2 $ lie group组结构。对于两个属的情况，通过构建二次不变形式，我们发现elelliptic $ \ wp $函数具有so（3,2）$ \ cong $ sp（4，$ \ r $）/$ \ z_2 $ lie组结构。利用二次不变的形式表明，与三属属的过性$ \ wp $具有SO（9,6）谎言组和/或其亚组结构。
We consider the generalized dual transformation for elliptic/hyperelliptic $\wp$ functions up to genus three. For the genus one case, from the algebraic addition formula, we deduce that the Weierstrass $\wp$ function has the SO(2,1) $\cong$ Sp(2,$\R$)/$\Z_2$ Lie group structure. For the genus two case, by constructing a quadratic invariant form, we find that hyperelliptic $\wp$ functions have the SO(3,2) $\cong$ Sp(4,$\R$)/$\Z_2$ Lie group structure. Making use of quadratic invariant forms reveals that hyperelliptic $\wp$ functions with genus three have the SO(9,6) Lie group and/or it's subgroup structure.
