Realizability of Two-dimensional Linear Groups over Rings of Integers of Algebraic Number Fields

被引：0

作者：

Dmitry Malinin

Freddy Van Oystaeyen

机构：

[1] Universität Mannheim,Fakultät für Mathematik und Informatik

[2] University of Antwerp,Department of Mathematics & Computer Science

来源：

Algebras and Representation Theory | 2011年 / 14卷

关键词：

Schur ring; Brauer reduction; Globally irreducible representations; Rings of integers; Algebraic number fields; 20G30; 20C10; 11R33; 11R29;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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, OK) 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).

引用

页码：201 / 211

页数：10

共 50 条

[1] Realizability of Two-dimensional Linear Groups over Rings of Integers of Algebraic Number Fields
Malinin, Dmitry
Van Oystaeyen, Freddy
[J]. ALGEBRAS AND REPRESENTATION THEORY, 2011, 14 (02) : 201 - 211
[2] Arithmetic of Linear Algebraic Groups over Two-dimensional Fields
Parimala, R.
[J]. PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS, VOL I: PLENARY LECTURES AND CEREMONIES, 2010, : 339 - 361
[3] Arithmetical birational invariants of linear algebraic groups over two-dimensional geometric fields
Borovoi, M
Kunyavskii, B
Gille, P
[J]. JOURNAL OF ALGEBRA, 2004, 276 (01) : 292 - 339
[4] An arithmetic site for the rings of integers of algebraic number fields
Schmidt, A
[J]. INVENTIONES MATHEMATICAE, 1996, 123 (03) : 575 - 610
[5] Subnormal Structure of Two-Dimensional Linear Groups over Full Rings
S. Tazhetdinov
[J]. Mathematical Notes, 2002, 71 : 844 - 850
[6] STRUCTURE OF TWO-DIMENSIONAL LINEAR-GROUPS OVER SEMILOCAL RINGS
ZHANG, YZ
[J]. KEXUE TONGBAO, 1982, 27 (09): : 1021 - 1021
[7] THE AUTOMORPHISMS OF TWO-DIMENSIONAL LINEAR-GROUPS OVER COMMUTATIVE RINGS
LI, F
REN, HS
[J]. CHINESE ANNALS OF MATHEMATICS SERIES B, 1989, 10 (01) : 50 - 57
[8] Subnormal structure of two-dimensional linear groups over full rings
Tazhetdinov, S
[J]. MATHEMATICAL NOTES, 2002, 71 (5-6) : 844 - 850
[9] Two-primary algebraic K-theory of rings of integers in number fields
Rognes, J
Weibel, C
Kolster, M
[J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 13 (01) : 1 - 54
[10] KI GROUPS OF RINGS OF ALGEBRAIC INTEGERS
HARRIS, B
SEGAL, G
[J]. ANNALS OF MATHEMATICS, 1975, 101 (01) : 20 - 33

← 1 2 3 4 5 →