On Alphabetic Presentations of Clifford Algebras and Their Possible Applications

TL;DR

This paper introduces a method for representing Clifford algebras using alphabetic words over small alphabets, exploring their properties and potential applications in mathematical and computational contexts.

Contribution

It formulates the problem of alphabetic representations of Clifford algebras and derives key properties and general results for these representations.

Findings

Defined the concept of alphabetic presentations for Clifford algebras

Derived main properties and theoretical results for these representations

Discussed potential applications in related fields

Abstract

In this paper we address the problem of constructing a class of representations of Clifford algebras that can be named "alphabetic (re)presentations". The Clifford algebras generators are expressed as m-letter words written with a 3-character or a 4-character alphabet. We formulate the problem of the alphabetic presentations, deriving the main properties and some general results. At the end we briefly discuss the motivations of this work and outline some possible applications.