2025/04/17 by Luc Ta, Ta, Luc · 4 citations
Engineering · Mathematics · #18B99 #20B25 #57K12 #Advanced Differential Equations and Dynamical Systems #Advanced Numerical Analysis Techniques #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Primary 20N02 #Quantum Algebra (math.QA) #Secondary 08A35
paper · pdf · doi:10.48550/arxiv.2504.12671
openalex publication_date 2025/04/17 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28
We study algebraic aspects of generalized Legendrian racks, which are nonassociative structures based on the Legendrian Reidemeister moves. We answer an open question characterizing the group of GL-structures on a given rack. As applications, we classify several infinite families of GL-racks. We also compute automorphism groups of dihedral GL-quandles. Then we compute the centers of the category of GL-racks and several of its full subcategories. We also construct an equivalence of categories between racks and GL-quandles. We also study tensor products of racks and GL-racks coming from universal algebra. Surprisingly, the categories of racks and GL-racks have tensor units. The induced symmetric monoidal structure on medial racks is closed, and similarly for medial GL-racks.