Article ID Journal Published Year Pages File Type
4589294 Journal of Algebra 2006 46 Pages PDF
Abstract

Let D be an arbitrary division ring and Pn(D) the set of all n×n idempotent matrices over D. Under some mild conditions, we give a complete description of maps on Pn(D) that preserve either commutativity, or order, or orthogonality. We give examples showing that our assumptions cannot be relaxed much further. As an application, we will prove a quaternionic analogue of Ovchinnikov's result that is important in quantum mechanics. Other applications of our theorems include results on automorphisms of operator and matrix semigroups, local automorphisms, linear preserver problems and geometry of matrices and Grassmannians.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory