Homomorphic images of affine quandles

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.