二面体群Grothendieck代数的Maschke定理

doi:10.6040/j.issn.1671-9352.0.2021.725

《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (2): 44-50.doi: 10.6040/j.issn.1671-9352.0.2021.725

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二面体群Grothendieck代数的Maschke定理

曹刘峰

扬州大学数学学院, 江苏扬州 225002

发布日期:2023-02-12
作者简介:曹刘峰(1995— ),男,博士研究生,研究方向为Hopf代数、代数表示理论、融合范畴等. E-mail:1204719495@qq.com
基金资助:
国家自然科学基金资助项目(11871063);江苏省研究生科研创新计划(KYCX22_3448)

Maschke theorem for the Grothendieck algebra of dihedral group

CAO Liu-feng

School of Mathematics, Yangzhou University, Yangzhou 225002, Jiangsu, China

Published:2023-02-12

摘要/Abstract

摘要： 设F是特征为0的代数闭域,n=2N+1为任一奇数,明确计算了阶为2n的二面体群D_n的Grothendieck环r(FD_n)的Casimir数为2n2,并且给出了对应的二面体群Grothendieck代数的Maschke定理。

关键词: 二面体群, Grothendieck环, Casimir数, Jacobson根

Abstract: Let F be an algebraically closed field with characteristic 0, and n=2N+1 be any odd number, we calculating the Casimir number of the Grothendieck ring r(FD_n) of the dihedral group D_n equals 2n2 explicitly. Furthermore, we give the Maschke theorem for the corresponding Grothendieck algebra of dihedral group.

Key words: dihedral group, Grothendieck ring, Casimir number, Jacobson radical

中图分类号:

O153.3

曹刘峰. 二面体群Grothendieck代数的Maschke定理[J]. 《山东大学学报(理学版)》, 2023, 58(2): 44-50.

CAO Liu-feng. Maschke theorem for the Grothendieck algebra of dihedral group[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(2): 44-50.

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二面体群Grothendieck代数的Maschke定理

Maschke theorem for the Grothendieck algebra of dihedral group

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