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Inner Automorphisms of an Abelian Extension of a Quandle

  • Yongju Bae (Department of Mathematics, Kyungpook National University) ;
  • Byeorhi Kim (Center for Research in Topology, POSTECH)
  • Received : 2023.08.12
  • Accepted : 2023.11.17
  • Published : 2023.12.31

Abstract

The inner automorphism groups of quandles are related to the classification problem of quandles. The inner automorphism group of a quandle is generated by inner automorphisms which are presented by columns in the operation table of the quandle. In this paper, we describe inner automorphisms of an abelian extension of a quandle by expressing columns of the operation table of the extended quandle as columns of the operation table of the original quandle. Such a description will be helpful in studying inner automorphism groups of abelian extensions of quandles.

Keywords

Acknowledgement

B. Kim was supported by National Research Foundation of Korea (NRF) Grant No. 2019R1A3B2067839 and Grant No. 2022R1A6A3A01086872.

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