New Lie-Algebraic and Quadratic Deformations of Minkowski Space from Twisted Poincare Symmetries

TL;DR

This paper introduces new classes of twisted Poincaré symmetries leading to Lie-algebraic and quadratic deformations of Minkowski space, expanding the understanding of noncommutative spacetime structures.

Contribution

It presents novel two-parameter Lie-algebraic and quadratic deformations of Minkowski space derived from twisted Poincaré symmetries, including explicit star-products and algebraic structures.

Findings

Defined new Lie-algebraic noncommutative Minkowski spaces.

Constructed quadratic deformations of Minkowski spacetime.

Described the associated deformed Poincaré groups.

Abstract

We consider two new classes of twisted D=4 quantum Poincar\'{e} symmetries described as the dual pairs of noncocommutative Hopf algebras. Firstly we investigate a two-parameter class of twisted Poincar\'{e} algebras which provide the examples of Lie-algebraic noncommutativity of the translations. The corresponding associative star-products and new deformed Lie-algebraic Minkowski spaces are introduced. We discuss further the twist deformations of Poincar\'{e} symmetries generated by the twist with its carrier in Lorentz algebra. We describe corresponding deformed Poincar\'{e} group which provides the quadratic deformations of translation sector and define the quadratically deformed Minkowski space-time algebra.