• Augmentation quotients for real representation rings of cyclic groups

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    • Keywords


      Cyclic group; real representation; augmentation ideal; augmentation quotient

    • Abstract


      Denote by $C_{m}$ the cyclic group of order $m$. Let $\mathcal{R}(C_{m})$ be its real representation ring, and $\Delta(C_{m})$ its augmentation ideal. In this paper, we give an explicit $\mathbb{Z}$-basis for the $n$-th power $\Delta^{n}(C_{m})$ and determine the isomorphism class of the $n$-th augmentation quotient $\Delta^{n}(C_{m})/\Delta^{n+1}(C_{m})$ for each positive integer $n$.

    • Author Affiliations



      1. School of Mathematics, Hefei University of Technology, Hefei 230009, China
      2. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China
    • Dates

  • Proceedings – Mathematical Sciences | News

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