Projective Brauer Theory

Abstract

In this article, we define and study a new concept of projective Brauer characters. Following the direct approach as taken in Navarro (1998) and Isaacs (1975), we study the resulting projective blocks of projective Frobenius characters and projective Brauer characters of a given group determined by certain linkage condition as an introduction to a projective extension of classic Brauer theory.

Key Words:

• α-Blocks of projective characters
• α-Decomposition matrix
• α-Regular elements
• Block idempotents
• Central characters
• Projective Brauer characters
• Projective representations
• Standard cocycles
• Twisted group algebras

2000 Mathematics Subject Classification:

• 20C20
• 20C15

ACKNOWLEDGMENTS

This article was a part of the author's Ph.D. thesis completed in early 2002 at the University of Calgary. The author would like to thank his supervisor Dr. K. Varadarajan for his careful examinations and useful suggestions. The author would give most credit of this article to the original contributors such as Brauer, Osima, and many others, of modular representation theory. The author would also like to thank Prof. Chen Guiyun at Southwest (Normal) University in Chougqing for his help and for providing software when editing this article.

Notes

Communicated by S. K. Sehgal.