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We consider the generalized dual transformation for elliptic/hyperelliptic$\wp$ functions up to genus three. For the genus one case, from the algebraicaddition 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, byconstructing 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 subgroupstructure.

The Lie Group Structure of Elliptic/Hyperelliptic $\wp$ Functions