$\kappa$-Deformation of Poincar\'e Superalgebra with Classical Lorentz Subalgebra and its Graded Bicrossproduct Structure

TL;DR

This paper reformulates the $$-deformed $D=4$ Poincaré superalgebra to highlight its classical Lorentz subalgebra and demonstrates its structure as a graded bicrossproduct, with applications to $$-deformed superspace.

Contribution

It presents a new basis for the $$-deformed $D=4$ Poincaré superalgebra that reveals its graded bicrossproduct structure and shows its covariant action on $$-deformed superspace.

Findings

Reformulation of the superalgebra in a classical Lorentz basis

Identification of the graded bicrossproduct structure

Demonstration of covariance on $$-deformed superspace

Abstract

The $\kappa$-deformed $D=4$ Poincar{\'e} superalgebra written in Hopf superalgebra form is transformed to the basis with classical Lorentz subalgebra generators. We show that in such a basis the $\kappa$-deformed $D=4$ Poincare superalgebra can be written as graded bicrossproduct. We show that the $\kappa$-deformed $D=4$ superalgebra acts covariantly on $\kappa$-deformed chiral superspace.