Finite Groups over Arithmetical Rings and Globally Irreducible Representations

✍ Scribed by F. Van Oystaeyen; A.E. Zalesski ĭ

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 142 KB
• Volume: 215
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1998.7712

✦ Synopsis

Given the ring of integers R of an algebraic number field K, for which natural Ž . number n is there a finite group G ; GL n, R such that RG, the R-span of G, Ž . Ž . Ž . coincides with M n, R , the ring of n = n -matrices over R? Given G ; GL n, R Ž . we show that RG s M n, R if and only if the Brauer reduction of G modulo every prime is absolutely irreducible. In addition, the question above is fully answered if n is an odd prime. ᮊ 1999 Academic Press * This work is performed as a part of the INTAS project ''Noncommutative algebra and geometry with focus to representation theory.'' It was started when the second-named author visited the University of Antwerp.