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- W2963247823 abstract "The category of symmetric quandles is a Mal'tsev variety whose subvariety of abelian symmetric quandles is the category of abelian algebras. We give an algebraic description of the quandle extensions that are central for the adjunction between the variety of quandles and its subvariety of abelian symmetric quandles. (A3) (a b) c = (a c) (b c) and (a 1 b) 1 c = (a 1 c) 1 (b 1 c) (self-distributivity). This structure is of interest in knot theory, since the three axioms above correspond to the Reidemeister moves on oriented link diagrams. From a purely algebraic viewpoint, quandles capture the properties of group conjugation: given a group (G; ; 1), by dening the operations a b = b a b 1 and a 1 b = b 1 a b on the underlying set G one gets a quandle structure." @default.
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- W2963247823 date "2016-01-01" @default.
- W2963247823 modified "2023-09-26" @default.
- W2963247823 title "A characterization of central extensions in the variety of quandles" @default.
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