Clifford Algebras and Graphs

TL;DR

This paper introduces a method to associate Clifford algebras with graphs, explores their structures, and discusses applications to modeling representations of certain Lie groups, providing new insights into algebra-graph relationships.

Contribution

It presents a novel construction linking Clifford algebras to graphs and analyzes their structure and classification, with applications to Lie group representations.

Findings

Classification of graphs by Clifford algebra isomorphism

Examples illustrating algebra-graph correspondence

Potential applications to Lie group models

Abstract

I show how to associate a Clifford algebra to a graph. I describe the structure of these Clifford graph algebras and provide many examples and pictures. I describe which graphs correspond to isomorphic Clifford algebras and also discuss other related sets of graphs. This construction can be used to build models of representations of simply-laced compact Lie groups.