Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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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
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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.

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Acknowledgement

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

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