有限群的C*代数的K0群的构造

章佳维; 周国晖

doi:10.12066/j.issn.1007-2861.2269

上海大学学报(自然科学版) >

2025 , Vol. 31 >Issue 6: 1047 - 1056

DOI: https://doi.org/10.12066/j.issn.1007-2861.2269

数理化科学

有限群的C^*代数的K₀群的构造

章佳维 ,
周国晖

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上海大学理学院, 上海 200444

收稿日期: 2020-03-30

网络出版日期: 2020-09-17

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On the construction of K₀ group of C^*-algebra of flnite group

ZHANG Jiawei ,
CHAO Kuok Fai

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College of Sciences, Shanghai University, Shanghai 200444, China

Received date: 2020-03-30

Online published: 2020-09-17

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摘要

主要给出有限群G的C^*代数C^*(G)的K₀群的结构.通过C^*(G)的全体投射及群G的特征标表,计算对应的K群K₀(C^*(G)).

关键词： 有限群; C^*代数; K理论

本文引用格式

章佳维 , 周国晖 . 有限群的C^*代数的K₀群的构造[J]. 上海大学学报(自然科学版), 2025 , 31(6) : 1047 -1056 . DOI: 10.12066/j.issn.1007-2861.2269

Abstract

We construct the K₀-group of C^* algebra C^*(G) of finite group G. By investigating the projections of C^*(G) and the characters table of group G, we compute K₀(C^*(G)) explicitly.

Key words： finite group; C^*-algebra; K-theory

参考文献

[1] Fillmore P A. A user’s guide to operator algebras [M]. New York: Wiley, 1996.
[2] Arveson W. An invitation to C^*-algebras [M]. New York: Springer-Verlag, 1976: 1-39.
[3] Clare P, Crisp T, Higson N. Parabolic induction and restriction via C^*-algebras and Hilbert C^*-modules [J]. Composito Mathematics, 2016, 152(6): 1286-1318.
[4] Steinberg B. Representation theory of finite groups: an introductory approach [M]. New York: Springer-Verlag, 2012: 27-50.
[5] Chao K F, Wang H. Langlands’s functoriality for K-theory of C*-algebras [J]. Journal of Noncommutative Geometry, 2017, 11: 1001-1036.

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