Good involutions of twisted conjugation subquandles and Alexander quandles

2025/08/22 by Ta, Luc
#20K30 #57K12 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Primary 20N02 #Quantum Algebra (math.QA) #Secondary 20D45

paper · doi:10.48550/arxiv.2508.16772

Abstract

We completely describe good involutions of free quandles and subquandles of twisted conjugation quandles of groups, including all Alexander quandles. As an application, we enumerate good involutions of linear quandles, and we provide explicit mappings for those up to order 23 via a computer search. Along the way, we completely characterize connected, involutory Alexander quandles, which may be of independent interest.

Citations

• Graph quandles: Generalized Cayley graphs of racks and right quasigroups
• Generalized (co)homology of symmetric quandles over homogeneous Beck modules
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• Good involutions of generalized Alexander quandles
• Embedding Alexander quandles into groups
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• Subquandles of free quandles
• Colorings beyond Fox: the other linear Alexander quandles
• On connected component decompositions of quandles
• Symmetric Enhancements of Involutory Virtual Birack Counting Invariants
• Connected quandles and transitive groups
• Lie theory and coverings of finite groups
• Symmetric Extensions of Dihedral Quandles and Triple Points of Non-orientable Surfaces
• A classifying invariant of knots, the knot quandle

Related

• Embedding Alexander quandles into groups
• Good involutions of conjugation subquandles
• Good involutions of generalized Alexander quandles
• Linear extensions of multiple conjugation quandles and MCQ Alexander pairs
• Primitive quandles with alternating displacement group