On the symplectic structure of irreducible representation modules of the metacyclic group \(G=\langle a,b:a^ n=1,\;b^ 2=a^ t,\;bab^{-1}=a^ r\rangle\)
type: Item
instance of: scholarly article
title: On the symplectic structure of irreducible representation modules of the metacyclic group \(G=\langle a,b:a^ n=1,\;b^ 2=a^ t,\;bab^{-1}=a^ r\rangle\)
zbMATH Open document ID: 0846.20011
author: Gerhard Roesch
author: Kurt Rosenbaum
published in: Beiträge zur Algebra und Geometrie
publication date: 1996-09-29T00:00:00Z
full work available at URL: https://eudml.org/doc/233272
full work available at URL: no.2
review text: Let \(G=\langle a,b:a^n=1\), \(b^2=a^t\), \(bab^{-1}=a^r\rangle\) be a metacyclic group with \((r,n)=1\), \(n\mid t(r-1)\) and \(r^2\equiv 1\pod n\), \(\mathbb{C}\) the field of complex numbers and \(*\) an involution of the group algebra \(\mathbb{C} G\). The authors determine up to isometric isomorphy all nondegenerate skewsymmetric and \(*\)-invariant bilinear forms of irreducible \(\mathbb{C} G\)-modules.
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 15A63
zbMATH DE Number: 821692
zbMATH Keywords: metacyclic groups
zbMATH Keywords: involutions
zbMATH Keywords: group algebras
zbMATH Keywords: \(*\)-invariant bilinear forms
zbMATH Keywords: irreducible \(\mathbb{C} G\)-modules
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 821692