Augmentation quotients for real representation rings of cyclic groups

Proceedings of the Indian Academy of Sciences. Mathematical sciences

HANG LIU^2¹  SHAN CHANG^1² 

[1] School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China^2;School of Mathematics, Hefei University of Technology, Hefei 230009, China^1

关键词: Cyclic group;    real representation;    augmentation ideal;    augmentation quotient;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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 $n$.

【 授权许可】

CC BY