# One Parameter Family of Jordanian Twists

## TL;DR

This paper introduces a generalized Jordanian twist satisfying the 2-cocycle condition, providing explicit formulas for the star product and twisted coproduct, and connecting it to previous twists via a 1-cochain.

## Contribution

It presents a new explicit generalization of the Jordanian twist that satisfies key algebraic conditions and relates to existing twists through cochain twisting.

## Key findings

- The generalized twist satisfies the 2-cocycle condition.
- Explicit formulas for the star product and twisted coproduct are provided.
- The generalization coincides with a twist obtained by twisting the simple Jordanian twist.

## Abstract

We propose an explicit generalization of the Jordanian twist proposed in $r$-symmetrized form by Giaquinto and Zhang. It is proved that this generalization satisfies the 2-cocycle condition. We present explicit formulas for the corresponding star product and twisted coproduct. Finally, we show that our generalization coincides with the twist obtained from the simple Jordanian twist by twisting by a 1-cochain.