SciPost Phys. Proc. 14, 016 (2023) ·
published 23 November 2023

· pdf
We give a brief review on recent developments of $\mathbb{Z}_2^n$graded symmetry in physics in which hidden $\mathbb{Z}_2^n$graded symmetries and $\mathbb{Z}_2^n$graded extensions of known systems are discussed. This elucidates physical relevance of the $\mathbb{Z}_2^n$graded algebras. As an example of physically interesting algebra, we take $\mathbb{Z}_2^2$graded supersymmetry (SUSY) algebras and consider their irreducible representations (irreps). A list of irreps for ${\cal N} = 1, 2$ algebras is presented and as an application of the irreps, $\mathbb{Z}_2^2$graded SUSY classical actions are constructed.