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arXiv · 2512.00064

Witt type Realizations of 2-D Cayley-Klein Algebras with non-zero curvatures

Arindam Chakraborty
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Abstract

The article presents various Witt type vector field realizations of 2-D Cayley-Klein algebras with non-vanishing curvatures. The expressions of the vector fields involve Jacobi elliptic functions whose moduli are directly related to the parameters that appear in the corresponding matrix representation obtained from a bi-orthogonal set of vectors. First, the realizations are obtained with the values of the moduli lying in the unit interval (0, 1). The parameter of biorthogonality plays a crucial role in this context. Later, with the help of modular transformation, realizations involving arbitrary moduli have been obtained.

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Arindam Chakraborty. 2025-11-24. Witt type Realizations of 2-D Cayley-Klein Algebras with non-zero curvatures. https://arxiv.org/abs/2512.00064

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