Kyungpook Mathematical Journal

  • 제56권1호
  • /
  • Pages.1-27
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  • 2016
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Ternary Distributive Structures and Quandles

  • 투고 : 2015.02.27
  • 심사 : 2015.06.17
  • 발행 : 2016.03.23
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초록

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.

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참고문헌

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