A N-extended version of superalgebras in D=3,9 mod 8

TL;DR

This paper explores generalized superalgebras with tensor p-form operators in specific odd dimensions, establishing conditions for their existence and explicitly solving for certain key cases.

Contribution

It introduces a unified framework for superalgebras with tensor operators in D=2n+1 dimensions and explicitly solves for low-dimensional cases.

Findings

Generalized superalgebras with tensor p-forms are characterized by generalized Jacobi identities.

Explicit solutions are provided for D=3, 9, 11 dimensions.

Conditions for the existence of these superalgebras are established and solved.

Abstract

A set of generalized superalgebras containing arbitrary tensor p-form operators is considered in dimensions $D=2n+1$ for $n=1,4 mod 4$ and the general conditions for its existence expressed in the form of generalized Jacobi identities is established. These are then solved in a univoque way and some lowest dimensional cases $ D= 3, 9, 11 $ of possible interest are made explicit.