Homomorphic images of affine quandles
P\v{r}emysl Jedli\v{c}ka, David Stanovsk\'y
TL;DR
This paper characterizes homomorphic images of affine quandles through properties of their displacement groups and affine meshes, providing algorithms for recognition and explicit constructions of covering affine quandles.
Contribution
It offers a novel two-fold characterization of homomorphic images of affine quandles and develops efficient algorithms for their recognition and construction.
Findings
Characterization via displacement group properties
Characterization via affine mesh properties
Efficient algorithms for recognition and construction
Abstract
We are interested in abstract conditions that characterize homomorphic images of affine quandles. Our main result is a two-fold characterization of this class: one by a property of the displacement group, the other one by a property of the corresponding affine mesh. As a consequence, we obtain efficient algorithms for recognizing homomorphic images of affine quandles, including an efficient explicit construction of the covering affine quandle.
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