An embedding of spherical quandles into Lie groups

2026/03/31 by Ayu Suzuki, Kentaro Yonemura
Mathematics · #math.GT #msc:20N02 #msc:57K12 #msc:53C35

paper · pdf

arxiv created 2026/08/03 · arxiv updated 2026/08/05

Abstract

We construct smooth embeddings of spherical quandles into conjugation quandles of Lie groups, where the ambient Lie groups can be taken to be orthogonal, Spin, or Pin groups. Moreover, in dimensions 1 and 3, we compare our embeddings with those due to Bergman and Akita.

Citations

• On embeddings of homogeneous quandles
• Embedding Alexander quandles into groups
• Central extensions of groups and adjoint groups of quandles
• Symplectic Group Actions and Covering Spaces
• Quandle coverings and their Galois correspondence
• Surface-Knots in 4-Space
• A classifying invariant of knots, the knot quandle
• Differential Geometry, Lie Groups, and Symmetric Spaces