Creating Infinitesimal Generators And Robust Messages With Adinkras

TL;DR

This paper introduces a novel graph-based framework using Adinkras and Baobabs to represent Lie superalgebras, error correction codes, and logical circuits, expanding their applications in mathematics and information theory.

Contribution

It generalizes Adinkras and Baobabs to all finite-dimensional Lie superalgebras and demonstrates their use in error correction and logical circuit design.

Findings

Adinkras can represent all finite-dimensional Lie superalgebras.

Baobabs serve as subgraphs capturing degrees of freedom.

Adinkras can implement forward error correction and erasure correction.

Abstract

Adinkras are graphs that can describe off-shell supermultiplets in 1 dimension with a Lie superalgebra known as Garden algebra. In this paper, I show that the degrees of freedom of the adinkra can be represented by a subgraph called a baobab. Because the structure of adinkras and baobabs are very general, I will show that all finite-dimensional Lie superalgebras can be similarly described by more general Lie adinkras and Lie baobabs. Furthermore, it will be shown that adinkras can represent forward error correction block codes, and bit erasures in Garden algebra adinkras can be corrected using logic circuits derived from baobabs.