Realizability of two-dimensional linear groups over rings of integers of algebraic number fields

Dmitry Malinin, Freddy Van Oystaeyen

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

Given the ring of integers OK of an algebraic number field K, for which natural numbers n there exists a finite group G ⊂ GL(n, O K) such that OKG, the OK-span of G, coincides with M(n, OK), the ring of (n×n)-matrices over OK? The answer is known if n is an odd prime. In this paper we study the case n = 2; in the cases when the answer is positive for n = 2, for n = 2m there is also a finite group G ⊂ GL(2m, OK) such that OKG = M(2m, OK).

Original languageEnglish
Pages (from-to)201-211
Number of pages11
JournalAlgebras and Representation Theory
Volume14
Issue number2
DOIs
Publication statusPublished - Apr 2011
Externally publishedYes

Keywords

  • Algebraic number fields
  • Brauer reduction
  • Globally irreducible representations
  • Rings of integers
  • Schur ring

ASJC Scopus subject areas

  • General Mathematics

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