Search results for " toroidal Lie groups"

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The periods of the generalized Jacobian of a complex elliptic curve

2015

Abstract We show that the toroidal Lie group G = ℂ2/Λ, where Λ is the lattice generated by (1, 0), (0, 1) and (τ̂, τ͂), with τ̂ ∉ ℝ, is isomorphic to the generalized Jacobian JL of the complex elliptic curve C with modulus τ̂, defined by any divisor class L ≡ (M) + (N) of C fulfilling M − N = [℘ (τ͂) : ℘´(τ͂) : 1] ∈ C. This follows from an apparently new relation between the Weierstrass sigma and elliptic functions.

Elliptic curve point multiplicationQuarter periodGeneralized JacobianModular elliptic curveJacobian curveMathematical analysisHessian form of an elliptic curveGeometry and TopologyGeneralized Jacobians toroidal Lie groupsSettore MAT/03 - GeometriaTripling-oriented Doche–Icart–Kohel curveMathematicsJacobi elliptic functions
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