Models of abstract and real systems based on broken symmetry group

Abstract

This article shows that symmetry groups as well as broken symmetry groups in natural and abstract mathematical may be used as models of development and evolution objects while describing the states and transformations of such systems. It also demonstrates “visualization” methods of PbTe nanostructures, ZN arithmetic, Galois group for the roots of a fourth degree polynomial, and DNA structure in the framework of category theory.