Complete Order Equivalence of Spin Unitaries

Abstract

The main objective of this thesis is to explore linear spaces of matrices and linear maps on matrix spaces that arise from spin systems, or spin unitaries, which are finite sets S of selfadjoint unitary matrices such that any two distinct unitaries in S anticommute. We are interested in examining finite-dimensional spin unitaries obtained from spin systems and complete order isomorphisms between the operator systems associated with spin systems.