Combinatorial approaches to the unit groups of Clifford algebras, II

Abstract

This is the second part of a two-part paper intended to introduce the use of Latin square and quasigroup techniques in a combinatorial approach to the unit groups of Clifford algebras. The aim of this part is to apply the techniques to a detailed study of the 32-element unit group of the real Clifford algebra of Minkowski spacetime, which we describe as the Pauli hull. This important special case deserves attention, both because of its connections with special relativity, and also as a home for multiple copies of the Pauli group of quantum information theory. Particular attention focuses on the automorphism group of the Pauli hull, and on the configurations of the copies of the Pauli group within the Pauli hull.