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Augmentation quotients for real representation rings of cyclic groups

  • Shan Chang
  • Hang Liu
Article

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.

Keywords

Cyclic group real representation augmentation ideal augmentation quotient 

2010 Mathematics Subject Classification

16S34 20C05 

Notes

Acknowledgements

The first author (SC) was supported by the NSFC (Nos 11226066 and 11401155) and the Natural Science Foundation of Anhui Province (No. 1308085QA01) and the second author (HL) was supported by the Fundamental Research Funds for the Central Universities (Nos GK20160311 and GK201803007) and NSFC (No. 11726606).

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Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.School of MathematicsHefei University of TechnologyHefeiChina
  2. 2.School of Mathematics and Information ScienceShaanxi Normal UniversityXi’anChina

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