ON THE CLASSIFICATION OF QUANDLES OF LOW ORDER

DOI10.1142/S0218216512500885zbMath1333.57026arXiv1105.5341OpenAlexW3104983658MaRDI QIDQ2890235

Leandro Vendramin

Publication date: 8 June 2012

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.5341

zbMATH Keywords

transitive groupsquandlescomputer software

Mathematics Subject Classification ID

Related Items (23)

Tensor products of quandles and 1-handles attached to surface-links ⋮ Quandle colorings of knots and applications ⋮ Relations between quandle extensions and group extensions ⋮ Divisibility relations for the dimensions and Hilbert series of Nichols algebras of non-Abelian group type. ⋮ Connected quandles and transitive groups ⋮ Enumerating finite racks, quandles and kei ⋮ Algebraic properties of quandle extensions and values of cocycle knot invariants ⋮ Nichols algebras with many cubic relations over small and dihedral quandles. ⋮ Enumeration of racks and quandles up to isomorphism ⋮ Quandle identities and homology ⋮ Computing with knot quandles ⋮ Virtual link and knot invariants from non-abelian Yang-Baxter 2-cocycle pairs ⋮ Simply connected latin quandles ⋮ Applications of self-distributivity to Yang–Baxter operators and their cohomology ⋮ On the lattice of subracks of the rack of a finite group ⋮ RiG ⋮ Flat connected finite quandles ⋮ General constructions of biquandles and their symmetries ⋮ Higher arity self-distributive operations in Cascades and their cohomology ⋮ Canonical Forms for Operation Tables of Finite Connected Quandles ⋮ Positive quandle homology and its applications in knot theory ⋮ Nichols algebras with many cubic relations ⋮ Computations of quandle 2-cocycle knot invariants without explicit 2-cocycles

Uses Software

• GAP

Cites Work

• Nichols algebras of group type with many quadratic relations.
• Pointed Hopf algebras over the sporadic simple groups.
• Simple quandles
• A classifying invariant of knots, the knot quandle
• From racks to pointed Hopf algebras
• The Betti numbers of some finite racks
• Constructing transitive permutation groups.
• Matrices and finite quandles
• The rack space
• TOWARD A CLASSIFICATION OF FINITE QUANDLES
• The Transitive Permutation Groups of Degree 32
• RACKS AND LINKS IN CODIMENSION TWO
• Quandle cohomology and state-sum invariants of knotted curves and surfaces
• James bundles
• Indecomposable set-theoretical solutions to the quantum Yang-Baxter equation on a set with a prime number of elements

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