Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Arindam Chakraborty

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.

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

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.

Paper Structure

This paper contains 4 sections, 1 theorem, 8 equations.

Table of Contents

  1. Introduction
  2. Auerbach bi-orthogonal system and deformed $\mathfrak{so}(2, 1)$ algebra
  3. Differential realization of deformed $\mathfrak{so}(2, 1)$ and Jacobi elliptic functions
  4. Conclusion

Key Result

Theorem 1

Given a pair of vectors $\{\vert v_j\rangle : j=1,2\}$ and an invertible hermitian operator $T$ relative to the relevant inner product, the set $\{\vert\phi_j\rangle= T \vert v_j\rangle: j=1, 2\}$ and $\{\vert\chi_j\rangle= (T^{-1})^\dagger\vert v_j\rangle: j=1, 2\}$ constitute bi-orthogonal system

Theorems & Definitions (3)

  • Definition 1
  • Theorem 1
  • Remark 1