Semi-simple extension of the (super)Poincar\'e algebra

TL;DR

This paper introduces a semi-simple tensor extension of the Poincaré algebra applicable in any dimension and develops a supersymmetric generalization specifically for four dimensions, expanding the algebraic framework of spacetime symmetries.

Contribution

It presents a new semi-simple tensor extension of the Poincaré algebra for arbitrary dimensions and constructs a supersymmetric version in four dimensions, advancing algebraic approaches in theoretical physics.

Findings

Proposed a semi-simple tensor extension of the Poincaré algebra for all dimensions.

Constructed a supersymmetric extension in four dimensions.

Enhanced the algebraic structure underlying spacetime symmetries.

Abstract

A semi-simple tensor extension of the Poincar\'e algebra is proposed for the arbitrary dimensions $D$. A supersymmetric also semi-simple generalization of this extension is constructed in the D=4 dimensions. This paper is dedicated to the memory of Anna Yakovlevna Gelyukh.