Combinatorial approaches to the unit groups of Clifford algebras, I

Abstract

This is the first part of a two-part paper introducing the application of Latin square and quasigroup techniques within a combinatorial approach to the unit groups of Clifford algebras. The two fundamental tools employed are a theorem showing that each unit group of a real Clifford algebra appears as a subgroup inside the multiplication group of a quasigroup, and the recently developed combinatorial theory of supersymmetry, which leads to a more uniform construction of the unit groups than is possible with the central product of groups.