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Brauer Characters and Grothendieck Rings

Published online by Cambridge University Press:  20 November 2018

B. M. Puttaswamaiah
B. M. Puttaswamaiah*
Affiliation:
Carleton University, Ottawa, Ontario
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Let G be a group of finite order g, A a splitting field of G of characteristic p (which may be 0) and R = AG the group algebra of G over A. In [2], the author studied some of the properties of the Grothendieck ring K(R) of the category of all finitely generated R-modules, and derived a number of consequences. This paper continues the study carried out in [2]. The study is concerned with the structure and irreducible representations of K(R). The ring K(R) is proved to be semisimple and the primitive idempotents of K(R) are explicitly constructed. If the ring K(R) is identified with the ‘algebra of representations', then Robinson's idempotent [3; 4; 5] follow from our description as a special case.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 5 , 01 October 1975 , pp. 1025 - 1028
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Curtis, C. W. and Reiner, I., Representation theory of finite groups and associative algebras (Interscience, New York, 1962), pp. 144-145 and pp. 598–600.Google Scholar
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