Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2017; 54(5): 1757-1771

Online first article July 17, 2017      Printed September 30, 2017

https://doi.org/10.4134/BKMS.b160742

Copyright © The Korean Mathematical Society.

Hilbert's Theorem 90 for non-compact groups

Marat Rovinsky

National Research University Higher School of Economics

Abstract

Let $K$ be a field and $G$ be a group of its automorphisms. It follows from Speiser's generalization of Hilbert's Theorem 90, \cite{Speiser} that any $K$-{\it semilinear} representation of the group $G$ is isomorphic to a direct sum of copies of $K$, if $G$ is finite. In this note three examples of pairs $(K,G)$ are presented such that certain irreducible $K$-semilinear representations of $G$ admit a simple description: (i) with precompact $G$, (ii) $K$ is a field of rational functions and $G$ permutes the variables, (iii) $K$ is a universal domain over field of characteristic zero and $G$ its automorphism group. The example (iii) is new and it generalizes the principal result of \cite{adm}.

Keywords: non-compact groups

MSC numbers: 14C15, 14F20, 14F43, 20B27, 20C32

Stats or Metrics

Share this article on :

Related articles in BKMS