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Keywords:
loop; right loop; left loop; commutator; associator
loop; right loop; left loop; commutator; associator
Summary:
Various commutators and associators may be defined in one-sided loops. In this paper, we approximate and compare these objects in the left and right loop reducts of a Catalan loop. To within a certain order of approximation, they turn out to be quite symmetrical. Using the general analysis of commutators and associators, we investigate the structure of a specific Catalan loop which is non-commutative, but associative, that appears in the original number-theoretic application of Catalan loops.
References:
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[3] Coxeter H.S.M., Moser W.O.J.: Generators and Relations for Discrete Groups. Springer, Berlin, 1957. MR 0088489 | Zbl 0487.20023
[4] Long L., Smith J.D.H.: Catalan loops. preprint, 2009.
[5] Mac Lane S.: Homology. Springer, Berlin, 1963. Zbl 0818.18001
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