$κ$-Deformation of Poincaré Superalgebra with Classical Lorentz Subalgebra and its Graded Bicrossproduct Structure

Abstract

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