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Abstract We show that the toroidal Lie group G = ℂ 2 /Λ, where Λ is the lattice generated by (1, 0), (0, 1) and (τ̂, τ͂), with τ̂ ∉ ℝ, is isomorphic to the generalized Jacobian J L of the complex elliptic curve C with modulus τ̂, defined by any divisor class L ≡ (M) + (N) of C...
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