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Ternary Distributive Structures and Quandles
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  • Journal title : Kyungpook mathematical journal
  • Volume 56, Issue 1,  2016, pp.1-27
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2016.56.1.1
 Title & Authors
Ternary Distributive Structures and Quandles
Elhamdadi, Mohamed; Green, Matthew; Makhlouf, Abdenacer;
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 Abstract
We introduce a notion of ternary distributive algebraic structure, give examples, and relate it to the notion of a quandle. Classification is given for low order structures of this type. Constructions of such structures from 3-Lie algebras are provided. We also describe ternary distributive algebraic structures coming from groups and give examples from vector spaces whose bases are elements of a finite ternary distributive set. We introduce a cohomology theory that is analogous to Hochschild cohomology and relate it to a formal deformation theory of these structures.
 Keywords
Ternary;distributivity;quandle;cohomology;deformation;
 Language
English
 Cited by
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