Annotating Lattice Orbifolds with Minimal Acting Automorphisms

Context and lattice orbifolds have been discussed by M. Zickwolff [1,2], B. Ganter and D. Borchmann[3,4]. Preordering the folding automorphisms by set inclusion of their orbits gives rise to further development. The minimal elements of this preorder have a prime group order and any group element can be dissolved into the product of group elements whose group order is a prime power. This contribution describes a way to compress an orbifold annotation to sets of such minimal automorphisms. This way a hierarchical annotation is described together with an interpretation of the annotation. Based on this annotation an example is given that illustrates the construction of an automaton for certain pattern matching problems in music processing.