Abstract
We use the structural aspects of the f-quandle theory to classify, up to isomorphisms, all f-quandles of order n. The classification is based on an effective algorithm that generate and check all f-quandles for a given order. We also include a pseudocode of the algorithm.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Carter, J.S., Crans, A.S., Elhamdadi, M., Saito, M.: Cohomology of categorical self-distributivity. J. Homotopy Relat. Struct. 3(1), 13–63 (2008)
Carter, J.S., Crans, A., Elhamdadi, M., Gra\(\tilde{n}\)a, M., Saito, M.: Cocycle knot invariants from quandle modules and generalized quandle homology. Osaka J. Math 42(3), 499–541 (2005)
Churchill, I.R.U., Elhamdadi, M., Green, M., Makhlouf, A.: f-racks, f-quandles, their extensions and cohomolog. J. Algebra Appl. 16(6) (2017)
Churchill, I.R.U., Elhamdadi, M., Green, M., Makhlouf, A.: Ternary and \(n\)-ary \(f\)-distributive structures. Open Math. 16, 32–45 (2018)
Churchill, I.R.U., Elhamdadi, M., Fernando, N.: The cocycle structure of the Alexander \(f\)-quandles on finite fields. J. Algebra Appl. 17(10) (2018)
Elhamdadi, M., Moutuou, E.M.: Foundations of topological racks and quandles. J. Knot Theory Ramif. 25(3) (2016)
Elhamdadi, M., Nelson, S.: Quandles—an introduction to the algebra of knots. In: American Mathematical Society, Providence, RI, vol. 74 (2015)
Elhamdadi, M., Macquarrie, J., Restrepo, R.: Automorphism groups of quandles. J. Algebra Appl. 11(1) (2012)
Fenn, R.: Rourke, Colin: Racks and links in codimension two. J. Knot Theory Ramif. 1(4), 343–406 (1992)
Hartwig, J.T., Larsson, D., Silvestrov, S.D.: Deformations of Lie algebras using \(\sigma \)-derivations. J. Algebra 295(2), 314–361 (2006)
Joyce, D.: A classifying invariant of knots, the knot quandle. J. Pure Appl. Algebra 23(1), 37–65 (1982)
Makhlouf, A., Silvestrov, S.D.: Hom-algebra structures. J. Gen. Lie Theory Appl. 2(2), 51–64 (2008)
Matveev, S.V.: Distributive groupoids in knot theory. Mat. Sb. (N.S.) 119(161), 78–88, 160 (1982)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Churchill, I.R., Elhamdadi, M., Van Kempen, N. (2020). On the Classification of f-Quandles. In: Silvestrov, S., Malyarenko, A., Rančić, M. (eds) Algebraic Structures and Applications. SPAS 2017. Springer Proceedings in Mathematics & Statistics, vol 317. Springer, Cham. https://doi.org/10.1007/978-3-030-41850-2_14
Download citation
DOI: https://doi.org/10.1007/978-3-030-41850-2_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-41849-6
Online ISBN: 978-3-030-41850-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)