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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Presented by V. Lebed.
The authors wish to dedicate the paper to the memory of Patrick Dehornoy who was one of the most inspiring guides through the world of self-distributivity.
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This article is part of the topical collection “In memory of Patrick Dehornoy” edited by V. Lebed.
The David Stanovský was partly supported by the GAČR grant 18-20123S.
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Jedlička, P., Stanovský, D. Homomorphic images of affine quandles. Algebra Univers. 82, 43 (2021). https://doi.org/10.1007/s00012-021-00732-7
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DOI: https://doi.org/10.1007/s00012-021-00732-7