Supersymmetry algebra cohomology IV: Primitive elements in all dimensions from D=4 to D=11

TL;DR

This paper systematically derives the primitive elements of supersymmetry algebra cohomology across dimensions D=4 to D=11, unifying previous results and extending them through dimensional methods for various signatures and supersymmetries.

Contribution

It provides a comprehensive and uniform derivation of primitive elements in supersymmetry algebra cohomology for all relevant dimensions from D=4 to D=11, including all signatures and supersymmetries.

Findings

Unified notation for cohomology elements

Explicit primitive elements for D=5 to D=11

Dimensional extension method from D=4

Abstract

The primitive elements of the supersymmetry algebra cohomology as defined in previous work are derived for standard supersymmetry algebras in dimensions D=5,...,11 for all signatures of the related Clifford algebras of gamma matrices and all numbers of supersymmetries. The results are presented in a uniform notation along with results of previous work for D=4, and derived by means of dimensional extension from D=4 up to D=11.