  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.
