Computing the associated groups of quandles with tools from group homology theory

2024/02/23 by Katsumi Ishikawa, Ishikawa, Katsumi · 1 citation
Computer Science · Mathematics · #20N02 (Primary) 20E22 #57K10 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2402.15417

openalex publication_date 2024/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a complete description of the associated group of any quandle as a central extension of the inner-automorphism group. As an application, we compute the second quandle homology groups of quandles of some families, including those of Alexander quandles.

Cited by

• Subracks and second homology of the conjugacy classes of finite projective special linear groups of degree two

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