# Interpolations between Jordanian Twists Induced by Coboundary Twists

## TL;DR

This paper introduces a generalized family of Jordanian twists that interpolate between simple twists, leading to new star products and realizations of noncommutative coordinates, with detailed exponential formulas and discussions on real forms.

## Contribution

It presents a novel generalization of Jordanian twists enabling interpolation between twists, expanding the framework for noncommutative geometry and quantum algebra.

## Key findings

- New family of Jordanian twists interpolates between simple twists
- Provides explicit exponential formulas for coproducts and star products
- Discusses real forms of the deformations

## Abstract

We propose a new generalisation of the Jordanian twist (building on the previous idea from [Meljanac S., Meljanac D., Pachol A., Pikutic D., J. Phys. A: Math. Theor. 50 (2017), 265201, 11 pages]). Obtained this way, the family of the Jordanian twists allows for interpolation between two simple Jordanian twists. This new version of the twist provides an example of a new type of star product and the realization for noncommutative coordinates. Real forms of new Jordanian deformations are also discussed. Exponential formulae, used to obtain coproducts and star products, are presented with details.