Jordan homomorphisms and harmonic mappings
Andrea Blunck, Hans Havlicek
TL;DR
This paper establishes a connection between Jordan homomorphisms of rings and harmonic mappings of projective lines, showing how algebraic structures induce geometric mappings and how these can be extended.
Contribution
It demonstrates that Jordan homomorphisms induce harmonic mappings between projective lines and provides methods for extending these mappings across multiple connected components.
Findings
Jordan homomorphisms induce harmonic mappings
Mappings can be extended to entire projective lines
Provides a framework linking algebraic and geometric structures
Abstract
We show that each Jordan homomorphism of rings gives rise to a harmonic mapping of one connected component of the projective line over into the projective line over . If there is more than one connected component then this mapping can be extended in various ways to a harmonic mapping which is defined on the entire projective line over .
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