Chirality in metric spaces. (English) Zbl 1476.51010
This paper generalizes the concept of chirality in chemistry to chirality in metric spaces which are not necessarily Euclidean. The group of isometric isomorphisms of a metric space is divided into direct isometries and indirect isometries. Then an object having no indirect symmetry is called chiral.
The author shows that this definition is equivalent to the usual definition if we consider an object in Euclidean space. Chirality of other objects such as strings, matrices and graphs is discussed. In conclusion we can consider a molecule in chemistry as an object in Euclidean space or the graph associated to the structural formula. One can be chiral while the other is not.
The author shows that this definition is equivalent to the usual definition if we consider an object in Euclidean space. Chirality of other objects such as strings, matrices and graphs is discussed. In conclusion we can consider a molecule in chemistry as an object in Euclidean space or the graph associated to the structural formula. One can be chiral while the other is not.
Reviewer: Elisa Hartmann (Göttingen)
Keywords:
chirality; metric space; distance; direct isometries; indirect isometries; indirect symmetryBiographic References:
Deza, MichelReferences:
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