Adinkras: Graphs of Clifford Algebra Representations, Supersymmetry, and Codes

TL;DR

This paper introduces Cliffordinkras, a graphical approach linking Clifford algebra representations to supersymmetry, error correcting codes, and other mathematical fields, providing a visual and geometric perspective.

Contribution

It presents Cliffordinkras as a new adaptation of Adinkras, connecting Clifford algebra representations with various mathematical disciplines in a visual framework.

Findings

Cliffordinkras relate to error correcting codes and algebraic topology.

They provide a geometric visualization of Clifford algebra representations.

The paper establishes foundational links between Cliffordinkras and multiple mathematical areas.

Abstract

An Adinkra is a graph from the study of supersymmetry in particle physics, but it can be adapted to study Clifford algebra representations. The graph in this context is called a Cliffordinkra, and puts some standard ideas in Clifford algebra representations in a geometric and visual context. In the past few years there have been developments in Adinkras that have shown how they are connected to error correcting codes, algebraic topology, algebraic geometry, and combinatorics. These connections also arise for Cliffordinkras. This paper introduces Cliffordinkras and describes the relationship to these subjects in that context. No previous knowledge of Adinkras and supersymmetry is assumed.