Poincare Algebra Extension with Tensor Generator

TL;DR

This paper introduces a tensor extension of the Poincaré algebra applicable to any dimension, constructs its Casimir operators, and explores a supersymmetric generalization in specific low dimensions.

Contribution

It presents a novel tensor extension of the Poincaré algebra and develops its Casimir operators, along with a supersymmetric generalization in dimensions 2, 3, and 4.

Findings

Tensor extension of Poincaré algebra proposed

Casimir operators constructed for the extension

Supersymmetric generalization identified in D=2,3,4

Abstract

A tensor extension of the Poincar\'e algebra is proposed for the arbitrary dimensions. Casimir operators of the extension are constructed. A possible supersymmetric generalization of this extension is also found in the dimensions $D=2,3,4$.