Quandle cohomology, extensions and automorphisms

Bardakov, Valeriy G.; Singh, Mahender

doi:10.1016/j.jalgebra.2021.06.016

Cited by 6 publications

(3 citation statements)

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“…We construct a generalization of Q-family of quandles. In [8] some general construction of quandles was suggested. Let us recall it.…”

Section: Preliminaries On Quandlesmentioning

confidence: 99%

“…Remark 3.11. Lemma 3.10 means that the map * f (g,h) : G × G → Map(X × X → X) satisfies the 2-cocycle condition, see, for example, [8]. Now let us present several examples of (G, f )-families of quandles.…”

Section: Definition 36 ([14]mentioning

confidence: 99%

“…During last years quandles have been studied as algebraic system without connection with knot theory. In particular, in [1,4,8,9] some constructions of quandles, extensions of quandles, automorphisms of quandles, and representations of quandles are studied. A good description of the algebraic theory of quandles can be found in the book [21].…”

Section: Introductionmentioning

confidence: 99%

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Multiplication of quandle structures

Bardakov¹,

Fedoseev²

2022

Preprint

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We generalise the construction of Q-family of quandles and G-family of quandles which were introduced in the paper of A. Ishii, M. Iwakiri, Y. Jang, K. Oshiro, and find connection with other constructions of quandles. We define a composition of quandl's structures, which are defined on the same set and find conditions under which this composition gives a quandle. Further we prove that under this multiplication we get a group and show that this group is abelian.

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“…We construct a generalization of Q-family of quandles. In [8] some general construction of quandles was suggested. Let us recall it.…”

Section: Preliminaries On Quandlesmentioning

confidence: 99%

Section: Definition 36 ([14]mentioning

confidence: 99%