A novel construction of Jacobi's elliptic functions from deformed Lie algebra

TL;DR

This paper introduces a new way to construct Jacobi's elliptic functions using a deformed Lie algebra, linking algebraic deformation to elliptic function properties.

Contribution

It presents a novel algebraic construction of elliptic functions based on a deformed Lie algebra and a bi-orthogonal system, connecting algebraic deformation with elliptic modulus.

Findings

Elliptic functions constructed from deformed Lie algebra.

Deformation parameter correlates with elliptic modulus.

New algebraic framework for elliptic functions.

Abstract

Jacobi's elliptic functions have been constructed from a deformed Lie algebra. The generators of the algebra have been obtained from a bi-orthogonal system. The deformation parameter resembles the modulus of the relevant elliptic functions.